MML Python, Ch.02 Linear Algebra.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import numpy.linalg as npl\n",
    "import pandas as pd\n",
    "from IPython.core.interactiveshell import InteractiveShell"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "InteractiveShell.ast_node_interactivity = \"all\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter 02. Linear Algebra\n",
    "## 2.1 Systems of Linear Equations\n",
    "### Example 2.2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1  1  1  3]\n",
      " [ 1 -1  2  2]\n",
      " [ 2  0  3  1]]\n",
      "Not solveable. Adding rows 1 and 2 contradicts row 3.\n"
     ]
    }
   ],
   "source": [
    "mat = np.vstack([[1,1,1],[1,-1,2],[2,0,3]])\n",
    "sol = np.vstack([3,2,1])\n",
    "try:\n",
    "    npl.solve(mat,sol)\n",
    "except:\n",
    "    print(np.hstack([mat,sol]))\n",
    "    print(\"Not solveable. Adding rows 1 and 2 contradicts row 3.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1  1  1  3]\n",
      " [ 1 -1  2  2]\n",
      " [ 0  1  1  2]]\n",
      "Solveable. Adding row 1 and 3 reveals x = 1, which fits with all rows.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[1.],\n",
       "       [1.],\n",
       "       [1.]])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mat = np.vstack([[1,1,1],[1,-1,2],[0,1,1]])\n",
    "sol = np.vstack([3,2,2])\n",
    "print(np.hstack([mat,sol]))\n",
    "print(\"Solveable. Adding row 1 and 3 reveals x = 1, which fits with all rows.\")\n",
    "npl.solve(mat,sol)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1  1  1  3]\n",
      " [ 1 -1  2  2]\n",
      " [ 2  0  3  5]]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/vb/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:4: FutureWarning: `rcond` parameter will change to the default of machine precision times ``max(M, N)`` where M and N are the input matrix dimensions.\n",
      "To use the future default and silence this warning we advise to pass `rcond=None`, to keep using the old, explicitly pass `rcond=-1`.\n",
      "  after removing the cwd from sys.path.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([4.45961819e+00, 1.45320528e+00, 3.12145137e-16])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mat = np.vstack([[1,1,1],[1,-1,2],[2,0,3]])\n",
    "sol = np.vstack([3,2,5])\n",
    "print(np.hstack([mat,sol]))\n",
    "npl.lstsq(mat,sol)[3] #Solution of coefficients multiplied with any # in R. I.e. Infinity of R solutions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Figure 2.3 \n",
    "The solution space of a system of two linear equations with two variables can be geometrically interepreted as the interesection of two lines. Every linear equation represents a line. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.pyplot import figure\n",
    "vals = np.linspace(-10,10,10000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.rcParams[\"figure.figsize\"] = (5,5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "eq0 = lambda x1: (5-4*x1)/4 # 4x1+4x2 = 5\n",
    "y0 = eq0(vals)\n",
    "\n",
    "eq1 = lambda x1: (1-2*x1)/-4 # 2x1-4x2 = 1\n",
    "y1 = eq1(vals)\n",
    "\n",
    "plt.plot(vals,y0,c=\"blue\")\n",
    "plt.plot(vals,y1,c=\"red\")\n",
    "idx = np.argwhere(np.diff(np.sign(y0 - y1))).flatten() # finds the intersection between two graphs\n",
    "plt.plot(vals[idx],y0[idx],'ko')\n",
    "plt.legend([\"4$x_1$+4$x_2$ = 5\",\"2$x_1$-4$x_2$ = 1\",str(np.round(vals[idx],3)) + str(np.round(y0[idx],3))]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.2 Matrices\n",
    "#### Figure 2.4\n",
    "*By stacking its columns, a matrix A can be represented as a long vector a.*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.2, 2. ],\n",
       "       [1.2, 2. ],\n",
       "       [1.2, 2. ],\n",
       "       [1.2, 2. ]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([[1.2],\n",
       "       [1.2],\n",
       "       [1.2],\n",
       "       [1.2],\n",
       "       [2. ],\n",
       "       [2. ],\n",
       "       [2. ],\n",
       "       [2. ]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = np.vstack([1.2,1.2,1.2,1.2])\n",
    "B = np.vstack([2,2,2,2])\n",
    "hAB = np.hstack([A,B])\n",
    "vAB = np.vstack([A,B])\n",
    "hAB\n",
    "vAB"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[9.6],\n",
       "       [9.6],\n",
       "       [9.6],\n",
       "       [9.6]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C = np.einsum('il,lj',A,B) \n",
    "# einsum takes a subscript that determines the operation of vector operations,\n",
    "# this one yields same result as np.dot(A.T,B)*np.ones(np.shape(A))\n",
    "C"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 2.3\n",
    "To compute element $c_{ij}$ we multiply the elements of the $i$th row of $A$ with the $j$th column of $B$ and sum them up. We will call this the dot product of the correspodning row and column. \n",
    "\n",
    "*Remark.* Matrices can only be multiplied if their neighborign dimensions match. For instance, an $n \\times k$ matrix $A$ can be multipled with a $k \\times m$ matrix $B$, but only from the left."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[1, 2, 3],\n",
       "        [3, 2, 1]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "matrix([[ 0,  2],\n",
       "        [ 1, -1],\n",
       "        [ 0,  1]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = np.matrix([[1,2,3],[3,2,1]])\n",
    "B = np.matrix([[0,2],[1,-1],[0,1]])\n",
    "A\n",
    "B"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[2, 3],\n",
       "        [2, 5]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dot(A,B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[ 6,  4,  2],\n",
       "        [-2,  0,  2],\n",
       "        [ 3,  2,  1]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dot(B,A)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Figure 2.5\n",
    "*Even if both matrix multiplciations $AB$ and $BA$ are defined, the dimensions of the results can be different.*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[ 6,  4,  2],\n",
       "        [-2,  0,  2],\n",
       "        [ 3,  2,  1]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "matrix([[2, 3],\n",
       "        [2, 5]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B@A\n",
    "A@B #as seen above"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 2.4 (Inverse Matrix)\n",
    "The matrices are inverse to each other sicne $AB = I = BA$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[1, 2, 1],\n",
       "        [4, 4, 5],\n",
       "        [6, 7, 7]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "matrix([[-7, -7,  6],\n",
       "        [ 2,  1, -1],\n",
       "        [ 4,  5, -4]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "matrix([[1, 0, 0],\n",
       "        [0, 1, 0],\n",
       "        [0, 0, 1]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = np.matrix([[1,2,1],[4,4,5],[6,7,7]])\n",
    "B = np.matrix([[-7,-7,6],[2,1,-1],[4,5,-4]])\n",
    "A\n",
    "B\n",
    "A*B\n",
    "(A*B == (B*A)).all() == ((B*A) == np.eye(A.shape[0])).all()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 2.5 (Distributivity)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(matrix([[1, 2],\n",
       "         [3, 4]]), 2, 3)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C = np.matrix([[1,2],[3,4]])\n",
    "lam = 2\n",
    "phi = 3\n",
    "C, lam, phi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[ 5, 10],\n",
       "        [15, 20]])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "matrix([[ 5, 10],\n",
       "        [15, 20]])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dot((lam+phi), C)\n",
    "temp0 = np.dot(phi, C)\n",
    "temp1 = np.dot(lam, C)\n",
    "temp0+temp1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.3 Solving Systems of Linear Equations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[ 1,  0,  8, -4],\n",
       "        [ 0,  1,  2, 12]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([[42],\n",
       "       [ 8]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = np.matrix([[1,0,8,-4],[0,1,2,12]])\n",
    "sol = np.vstack([42,8])\n",
    "A\n",
    "sol"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One approach is to zero out the third and fourth column and take advantage of the identity matrix embedded as columns 1 and 2. This only returns a particular solution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[42],\n",
       "        [ 8]])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dot(A,np.vstack([42,8,0,0]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another approach is to compose columns as vector operations of other columns, such as scalar multiplication and addition, and combine to find a general solution. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[0],\n",
       "        [0]])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Here column three is composed of col 1 and 2, and 3 is inverted.\n",
    "lam = 51345 # arbitrary scalar used to show the infinity of solutions.\n",
    "np.dot(A,lam*np.vstack([A[:,2],-1,0])) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[0],\n",
       "        [0]])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Here column four is composed of col 1 and 2, and 4 is inverted.\n",
    "np.dot(A,lam*np.vstack([A[:,3],0,-1])) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[42],\n",
       "        [ 8]])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dot(A,np.vstack([42,8,0,0])) + np.dot(A,lam*np.vstack([A[:,2],-1,0]))  + np.dot(A,lam*np.vstack([A[:,3],0,-1]))  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Because the above two vectors result in the 0 vector, they can be added to the particular solution and still yield the same result, meaning that the summation of the particular to the zeros, yields the general."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 2.6\n",
    "Elementary operations are key to solving systems of linear equations and involve the following.\n",
    "1. Exchange of two equations, or rows in the matrix.\n",
    "2. Multiplication of an equation, or row, with a constant $\\lambda \\in \\mathbb{R}$.\n",
    "3. Addition of two equation, or rows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-2,  4, -2, -1,  4],\n",
       "       [ 4, -8,  3, -3,  1],\n",
       "       [ 1, -2,  1, -1,  1],\n",
       "       [ 1, -2,  0, -3,  4]])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([[-3],\n",
       "       [ 2],\n",
       "       [ 0],\n",
       "       [50]])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([[-2,  4, -2, -1,  4, -3],\n",
       "       [ 4, -8,  3, -3,  1,  2],\n",
       "       [ 1, -2,  1, -1,  1,  0],\n",
       "       [ 1, -2,  0, -3,  4, 50]])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = 50 # for any arbitrary value a in R\n",
    "A = np.vstack([[-2,4,-2,-1,4],[4,-8,3,-3,1],[1,-2,1,-1,1],[1,-2,0,-3,4]])\n",
    "b = np.vstack([-3,2,0,a])\n",
    "A\n",
    "b\n",
    "Ab = np.hstack([A,b])\n",
    "Ab"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1, -2,  1, -1,  1,  0],\n",
       "       [ 4, -8,  3, -3,  1,  2],\n",
       "       [-2,  4, -2, -1,  4, -3],\n",
       "       [ 1, -2,  0, -3,  4, 50]])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Ab[[0,2]] = Ab[[2,0]] # Exchange of two equations. I.e. swap row 1 and 3.\n",
    "Ab"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1, -2,  1, -1,  1,  0],\n",
       "       [ 4, -8,  3, -3,  1,  2],\n",
       "       [-2,  4, -2, -1,  4, -3],\n",
       "       [ 0,  0, -1, -2,  3, 50]])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Ab[3] -= Ab[0] # Addition of two equation, or rows. Subtract row 1 from 4.\n",
    "Ab"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1, -2,  1, -1,  1,  0],\n",
       "       [ 4, -8,  3, -3,  1,  2],\n",
       "       [ 0,  0,  0, -3,  6, -3],\n",
       "       [ 0,  0, -1, -2,  3, 50]])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Ab[2] += 2*Ab[0] # Addition of two equation, or rows. Add 2 * row 1 to row 3.\n",
    "Ab"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1, -2,  1, -1,  1,  0],\n",
       "       [ 0,  0, -1,  1, -3,  2],\n",
       "       [ 0,  0,  0, -3,  6, -3],\n",
       "       [ 0,  0, -1, -2,  3, 50]])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Ab[1] -= 4*Ab[0] # Addition of two equation, or rows. Subtract 4 * row 1 to row 2\n",
    "Ab"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1, -2,  1, -1,  1,  0],\n",
       "       [ 0,  0, -1,  1, -3,  2],\n",
       "       [ 0,  0,  0, -3,  6, -3],\n",
       "       [ 0,  0,  0,  0,  0, 51]])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Ab[3] += -Ab[1] - Ab[2] # Addition of two equation, or rows. Add -Row 2 - Row 3\n",
    "Ab"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1., -2.,  1., -1.,  1.,  0.],\n",
       "       [ 0.,  0.,  1., -1.,  3., -2.],\n",
       "       [-0., -0., -0.,  1., -2.,  1.],\n",
       "       [ 0.,  0.,  0.,  0.,  0., 51.]])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Ab[1] *= -1 # Multiplication of an equation, or row, with a constant. Invert row 2\n",
    "Ab = Ab.astype(float)\n",
    "Ab[2] *= -1/3 # Multiplication of an equation, or row, with a constant. Divide row 3 by -3\n",
    "Ab "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that if a had been -51 we would have a solution, that is, the sum of the left hand side for the final row is 0, only if a is `-51`. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1., -2.,  1., -1.,  1.,  0.],\n",
       "       [ 0.,  0.,  1., -1.,  3., -2.],\n",
       "       [-0., -0., -0.,  1., -2.,  1.],\n",
       "       [ 0.,  0.,  0.,  0.,  0.,  0.]])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Ab[:,5][3] -= a+1\n",
    "Ab"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can see that for the first row, we can find a particular solution. \n",
    "**Incomplete.** Ambiguity on how the general solution was found. Worth expanding this exercise. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dot(Ab[0][:5],np.array([2,0,-1,1,0]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "# alternatively\n",
    "from sympy import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}-2 & 4 & -2 & -1 & 4 & -3\\\\4 & -8 & 3 & -3 & 1 & 2\\\\1 & -2 & 1 & -1 & 1 & 0\\\\1 & -2 & 0 & -3 & 4 & 50\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[-2,  4, -2, -1, 4, -3],\n",
       "[ 4, -8,  3, -3, 1,  2],\n",
       "[ 1, -2,  1, -1, 1,  0],\n",
       "[ 1, -2,  0, -3, 4, 50]])"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M = Matrix([[-2,4,-2,-1,4, -3],[4,-8,3,-3,1, 2],[1,-2,1,-1,1,0],[1,-2,0,-3,4,a]]) \n",
    "M"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(Matrix([\n",
       " [1, -2, 0, 0, -2, 0],\n",
       " [0,  0, 1, 0,  1, 0],\n",
       " [0,  0, 0, 1, -2, 0],\n",
       " [0,  0, 0, 0,  0, 1]]), (0, 2, 3, 5))"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M_rref = M.rref()\n",
    "M_rref"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 2.7 (Reduced Row Echelon Form)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1,  3,  0,  0,  3],\n",
       "       [ 0,  0,  1,  0,  9],\n",
       "       [ 0,  0,  0,  1, -4]])"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = np.vstack([[1,3,0,0,3],[0,0,1,0,9],[0,0,0,1,-4]])\n",
    "A"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "*Look for solutions of Ax = 0 by looking at non-pivot columns*.\n",
    "\n",
    "1. The 2nd column is 3 times the 1st column.\n",
    "2. To obtain 0 we subtract the 2nd column from three times the 1st column.\n",
    "3. The 5th column is our 2nd non-pivot. It can be expressed as 3 times the 1st pivot column,\n",
    "    9 times the 2nd pivot column, and -4 times the 3rd pivot column. \n",
    "4. Track the indices of the pivot columns and translate this into:\n",
    "    1. 3 times the 1st pivot column, \n",
    "    2. 0 times the 2nd column, (the 1st non-pivot)\n",
    "    3. 9 times the 3rd column, and (the 2nd pivot column)\n",
    "    4. -4 times the 4th column  (the 3rd pivot column)\n",
    "5. Subtract the 5th column to obtain 0. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True,  True,  True])"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A[:,1] == A[:,0]*3 #step 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 0])"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([[0],\n",
       "       [0],\n",
       "       [0]])"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A[:,0]*3 + A[:,1]*-1 #step 2\n",
    "A @ np.vstack([3,-1,0,0,0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 3,  9, -4])"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([ 3,  9, -4])"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A[:,4] #step 3\n",
    "A[:,0]*3 + A[:,2]*9 + A[:,3]*-4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3, 0, 0])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([0, 0, 0])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([0, 9, 0])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([ 0,  0, -4])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([0, 0, 0])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([[0],\n",
       "       [0],\n",
       "       [0]])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A[:,0]*3 #step 4\n",
    "A[:,1]*0\n",
    "A[:,2]*9\n",
    "A[:,3]*-4\n",
    "A[:,4] + A[:,4]*-1 #step 5\n",
    "A @ np.vstack([3,0,9,-4,-1])\n",
    "# Which leaves us with our solution of the vectors [3,-1,0,0,0],[3,0,9,-4,-1], \n",
    "# respectively scalable by lam 1 and 2."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 2.8 (Minus-1 Trick)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1,  3,  0,  0,  3],\n",
       "       [ 0,  0,  1,  0,  9],\n",
       "       [ 0,  0,  0,  1, -4]])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A1 = A\n",
    "A1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The trick is to have the diagonal have either 1 or -1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1,  3,  0,  0,  3],\n",
       "       [ 0, -1,  0,  0,  0],\n",
       "       [ 0,  0,  1,  0,  9],\n",
       "       [ 0,  0,  0,  1, -4],\n",
       "       [ 0,  0,  0,  0, -1]])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A1 = np.insert(A1,1,np.array([0,-1,0,0,0]),0)\n",
    "A1 = np.insert(A1,4,np.array([0,0,0,0,-1]),0)\n",
    "A1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Which gives us the solution from Example 2.7 above in columns 2 and 5."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 2.9 (Calculating an Inverse Matrix by Gaussian Elimination)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 0, 2, 0],\n",
       "       [1, 1, 0, 0],\n",
       "       [1, 2, 0, 1],\n",
       "       [1, 1, 1, 1]])"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([[1., 0., 0., 0.],\n",
       "       [0., 1., 0., 0.],\n",
       "       [0., 0., 1., 0.],\n",
       "       [0., 0., 0., 1.]])"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = np.vstack([[1,0,2,0],[1,1,0,0],[1,2,0,1],[1,1,1,1]])\n",
    "aug = np.eye(np.shape(A)[0])\n",
    "A\n",
    "aug"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 0., 2., 0., 1., 0., 0., 0.],\n",
       "       [1., 1., 0., 0., 0., 1., 0., 0.],\n",
       "       [1., 2., 0., 1., 0., 0., 1., 0.],\n",
       "       [1., 1., 1., 1., 0., 0., 0., 1.]])"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Aaug = np.hstack([A,aug])\n",
    "Aaug"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-1.,  2., -2.,  2.],\n",
       "       [ 1., -1.,  2., -2.],\n",
       "       [ 1., -1.,  1., -1.],\n",
       "       [-1.,  0., -1.,  2.]])"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "npl.inv(A) # Gaussian elimination as above, yields this as the RHS."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 0., 0., 0.],\n",
       "       [0., 1., 0., 0.],\n",
       "       [0., 0., 1., 0.],\n",
       "       [0., 0., 0., 1.]])"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#The inverse of a matrix is in essence the solution to the matrix given that it represents a system of equations. \n",
    "#This can be verified via AA^-1 = I\n",
    "np.dot(A,npl.inv(A))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.4 Vector Spaces\n",
    "\n",
    "One major idea in mathematics is the idea of “closure”. This is the question: What is the set of all things that can result from my proposed operations? In the case of vectors: What is the set of vectors that can result by\n",
    "starting with a small set of vectors, and adding them to each other and\n",
    "scaling them? This results in a vector space.\n",
    "\n",
    "A group is a set of elements and an operation defined on these elements that keeps some structure of the set intact. \n",
    "\n",
    "### Example 2.10 (Groups) \n",
    "*Book provides examples of sets and operations.* Might return to this and show how each example does or doesn't satisfy closure, associativity, neutrality, invertability.\n",
    "### Example 2.11 (Vector Spaces)\n",
    "*Book provides general example.*\n",
    "### Example 2.12 (Vector Subspaces)\n",
    "*Book provides general examples, except the reference to Figure 2.6.*\n",
    "#### Figure 2.6 \n",
    "*Not all subsets of $\\mathbb{R}^2$ are subspaces. In A and C, the closure property is violated , B does not contain 0. Only D is a subspace.*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.rcParams[\"figure.figsize\"] = (7,7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "'''\n",
    "\"In A and C, the closure property is violated\".\n",
    "\n",
    "For A this doesn't work because for any x and y within the vector space, \n",
    "multiplying x and y might not still be in the vector space. Ergo, closure violated. \n",
    "\n",
    "Of course, if A was a unit (1) vector, closure property would still hold. \n",
    "E.g.: .9 * .9 = smaller than .9; 1.1*1.1 = bigger than 1.1)\n",
    "\n",
    "For C, a shift could occur that bumps a vector outside of this vector space. \n",
    "'''\n",
    "\n",
    "origin = np.vstack([0,0])\n",
    "v = 1.5\n",
    "scale = v*10\n",
    "vec = np.array([v,0])\n",
    "vec1 = np.array([1.5,1.5])\n",
    "vec2 = np.array([0,1.5])\n",
    "plt.axis([-scale/2,scale/2,-scale/2,scale/2])\n",
    "plt.fill_between(np.linspace(-v,v,100),np.linspace(v,v,100),np.linspace(-v,-v,100)) # vector space\n",
    "plt.quiver(*origin, *vec, scale = scale)\n",
    "plt.quiver(*origin, *vec1, scale = scale, color = \"gold\")\n",
    "plt.quiver(*origin, *vec2, scale = scale, color = \"gold\")\n",
    "plt.quiver(*origin, *np.array(vec1*vec2), scale = scale,color = \"gold\") # operation on vec 1 with vec 2\n",
    "plt.title(\"A, Violates closure with vector operation.\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(np.linspace(-6,6,100),np.linspace(-6,4,100)+2)\n",
    "plt.plot(np.linspace(-6,6,100),np.linspace(0,0,100),color=\"k\")\n",
    "plt.plot(np.linspace(0,0,100),np.linspace(-6,6,100),color=\"k\")\n",
    "plt.scatter(0,0,color=\"k\")\n",
    "plt.title(\"B. Violates neutral element property.\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "xs = np.linspace(-6,6,100)\n",
    "y1 = np.linspace(-6*2,6*2,100)\n",
    "y2 = np.linspace(-6*5,6*5,100)\n",
    "\n",
    "plt.plot(xs,np.linspace(0,0,100),color=\"k\") #0\n",
    "plt.plot(np.linspace(0,0,100),np.linspace(-30,30,100),color=\"k\") #0\n",
    "plt.scatter(0,0,color=\"k\") #0\n",
    "\n",
    "plt.plot(xs,y1, color = \"k\")\n",
    "plt.plot(xs,y2, color = \"k\")\n",
    "\n",
    "plt.fill_between(xs,y1,y2) # vector space\n",
    "v1 = np.array([3,1.4]) # represents slope of vector\n",
    "v2 = np.array([2,1.4]) \n",
    "v3 = v2*v1\n",
    "\n",
    "plt.quiver(*origin,*v1,scale = scale, color = \"gold\") # v1\n",
    "plt.quiver(*origin,*v2,scale = scale, color = \"gold\") # v2\n",
    "plt.quiver(*origin,*v3,scale = scale, color = \"gold\") # v3\n",
    "plt.legend([\"v1:\"+str(v1),\"v2:\"+str(v2),\"v3:\"+str(v3)])\n",
    "plt.title(\"C. Violates closure with vector operation.\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(0,0)\n",
    "plt.title(\"D. Satisfies closure, associativity, neutrality, invertability.\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.5 Linear Independence\n",
    "Given a vector v1, that can be represented as some operation with another vector, v2, such as $\\times 2$, v1 and v2 are said to be linearly dependent. If v1 cannot be represented as an operation with another vector, v3, they are said to be linearly independent. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "origin = np.array([5,3])\n",
    "scale = 12.5\n",
    "\n",
    "v1 = np.array([-5,2])\n",
    "v2 = np.array([-2,-3]) \n",
    "v3 = -v2-v1 # Here V3 is composed of v2 and v1, so is said to be linearly dependent. \n",
    "\n",
    "plt.quiver(*origin, *v1, scale = scale, color = \"r\")\n",
    "plt.quiver(*origin+v1, *v2, scale = scale, color = \"g\")\n",
    "plt.quiver(*origin+v1+v2, *v3, scale = scale, color = \"b\")\n",
    "plt.quiver(*origin, *v2, scale = scale, color = \"g\")\n",
    "\n",
    "plt.legend([\"Nairobi -> Kampala\",\"Kampala -> Kigali\",\"Nairobi -> Kigali\",\"\"], loc = 3)\n",
    "plt.axis([-scale/2,scale/2,-scale/2,scale/2]);\n",
    "plt.title(\"Note: V3, Nairobi -> Kigali, is composed of V2 and V1.\")\n",
    "plt.suptitle(\"V1 and V2 independent, V3 dependent.\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 2.14"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1 & 1 & -1\\\\2 & 1 & -2\\\\-3 & 0 & 1\\\\4 & 2 & 1\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[ 1, 1, -1],\n",
       "[ 2, 1, -2],\n",
       "[-3, 0,  1],\n",
       "[ 4, 2,  1]])"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "(Matrix([\n",
       " [1, 0, 0],\n",
       " [0, 1, 0],\n",
       " [0, 0, 1],\n",
       " [0, 0, 0]]), (0, 1, 2))"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = Matrix([[1,1,-1],[2,1,-2],[-3,0,1],[4,2,1]])\n",
    "A\n",
    "A.rref()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Because every column is a pivot column, there is no non=trivial solution, thus $\\lambda_{1,2,3} = 0$, and the column vectors $x_{1,2,3}$ are linearly independent. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 2.15"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1 & -4 & 2 & 17\\\\-2 & -2 & 3 & -10\\\\1 & 0 & -1 & 11\\\\-1 & 4 & -3 & 1\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[ 1, -4,  2,  17],\n",
       "[-2, -2,  3, -10],\n",
       "[ 1,  0, -1,  11],\n",
       "[-1,  4, -3,   1]])"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "(Matrix([\n",
       " [1, 0, 0,  -7],\n",
       " [0, 1, 0, -15],\n",
       " [0, 0, 1, -18],\n",
       " [0, 0, 0,   0]]), (0, 1, 2))"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = Matrix([[1,-4,2,17],[-2,-2,3,-10],[1,0,-1,11],[-1,4,-3,1]])\n",
    "A\n",
    "A.rref()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Because the last column is not a pivod column, we know the system is non-trivially solvable, thus the column vectors $x_{1,2,3,4}$ are linearly dependent as we know $x_4$ can be expressed as a linear combination of $x_{1,2,3}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.6 Basis and Rank\n",
    "A basis is a set of vectors which are linearly independent and can be used to determine all vectors in a vector space.\n",
    "\n",
    "The total number of linearly independent columns of a matrix and the total number of linearly independent rows are always equal, this value is considered the rank of a matrix.\n",
    "\n",
    "### Example 2.16"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 0, 0],\n",
       "       [0, 1, 0],\n",
       "       [0, 0, 1]])"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([[1, 1, 1],\n",
       "       [0, 1, 1],\n",
       "       [0, 0, 1]])"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([[ 0.5,  1.8, -2.2],\n",
       "       [ 0.8,  0.3, -1.3],\n",
       "       [ 0.4,  0.3,  3.5]])"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "origin3D = np.array([0,0,0])\n",
    "basis3D1 = np.vstack([[1,0,0],[0,1,0],[0,0,1]]) #standard basis\n",
    "basis3D2 = np.vstack([[1,1,1],[0,1,1],[0,0,1]]) #b1, 2.79\n",
    "basis3D3 = np.vstack([[.5,1.8,-2.2],[.8,.3,-1.3],[.4,.3,3.5]]) #b2, 2.79\n",
    "bases = [basis3D1,basis3D2,basis3D3]\n",
    "basis3D1\n",
    "basis3D2\n",
    "basis3D3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "plt.rcParams[ \"figure.figsize\" ] = (10,10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.gca(projection = '3d')\n",
    "scale3D = 1\n",
    "ax.set_xlim3d(-scale3D,scale3D)\n",
    "ax.set_ylim3d(scale3D,-scale3D)\n",
    "ax.set_zlim3d(-scale3D,scale3D)\n",
    "\n",
    "c = [\"r\",\"g\",\"b\"]\n",
    "lw = [3,1.5,.25]\n",
    "for ind,base in enumerate(bases):\n",
    "    for j,v in enumerate(base):\n",
    "        ax.quiver(*origin3D,*base[:,j],length=scale3D/2, color=c[ind], linewidths=lw[ind])\n",
    "        \n",
    "plt.title(\"Example 2.16\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The above are examples of basis, a collection of vectors that can be used to represent other vectors in a space. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1 & 2 & 1\\\\2 & -1 & 1\\\\3 & 0 & 0\\\\4 & 2 & -4\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[1,  2,  1],\n",
       "[2, -1,  1],\n",
       "[3,  0,  0],\n",
       "[4,  2, -4]])"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "(Matrix([\n",
       " [1, 0, 0],\n",
       " [0, 1, 0],\n",
       " [0, 0, 1],\n",
       " [0, 0, 0]]), (0, 1, 2))"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = Matrix([[1,2,1],[2,-1,1],[3,0,0],[4,2,-4]])\n",
    "A\n",
    "A.rref()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The above matrix, $A$, is linearly independent as we can see that all column vectors are pivots, but is not a generating set, and thus not a basis for $\\mathbb{R}^4$, as a vector like $[1,0,0,0]^T$ is unobtainable from a combination of the column vectors in $A$. I.e. there exists no multiplication or addition between the column vectors that would create the linearly independent column vector $[1,0,0,0]^T$ shown in the above performed `rref()`. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 2.17 (Determining a Basis)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(Matrix([\n",
       " [1, 0, -1, 0],\n",
       " [0, 1,  2, 0],\n",
       " [0, 0,  0, 1],\n",
       " [0, 0,  0, 0],\n",
       " [0, 0,  0, 0]]), (0, 1, 3))"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = Matrix([[1,2,3,-1],[2,-1,-4,8],[-1,1,3,-5],[-1,2,5,-6],[-1,-2,-3,1]])\n",
    "A.rref()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The three pivot columns, $x_{1,2,4}$, determined by `rref()` can be used a basis, as they can only be solved with $\\lambda_{1,2,4} = 0$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 2.18 (Rank)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = Matrix([[1,0,1],[0,1,1],[0,0,0]])\n",
    "len(A.rref()[1]) #rank of this matrix = how many linearly independent columns or rows exist."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = Matrix([[1,2,1],[-2,-3,1],[3,5,0]])\n",
    "len(A.rref()[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.7 Linear Mappings\n",
    "Given two vectors and a function, if the function applied to the vectors either via application to each and then either added or multiplied, or in application to the vectors added or multiplied to each other, yield the same results, then we have a mapping function between vectors that is linear, also known as a linear map, also known as a homomorphism. \n",
    "\n",
    "Also, linear mappings can be considered injective, meaning there is strictly a one-to-one mapping from on space to another and that not all elements in the other have to have been mapped from the first  (one-to-one), surjective, meaning every element in the second space is mapped to (onto), or bijective, meaning there is a one to one mapping that maps all elements from A to all elements in B (both). "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 2.19 (Homomorphism)\n",
    "*Book provides general example for $\\mathbb{R}^2 \\rightarrow \\mathbb{C}$.*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Figure 2.8\n",
    "*Two different coordinate systems defined by two sets of basis vectors. A vector $x$ has different coordiante representations depending on which coordinate system is chosen.*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.rcParams[ \"figure.figsize\" ] = (5,5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "origin = np.array([0,0])\n",
    "standardBasis = np.vstack([[1,0],[0,1]])\n",
    "altBasis = np.vstack([[1.5,.75],[.25,1.5]])\n",
    "v1 = lambda b: np.dot(b,np.array([2,2]))\n",
    "scale = 10\n",
    "plt.axis([-scale/2,scale/2,-scale/2,scale/2])\n",
    "plt.quiver(*origin,*v1(standardBasis),scale=scale,color=\"k\")\n",
    "plt.quiver(*origin,*v1(altBasis),scale=scale,color=\"g\")\n",
    "plt.quiver(*origin,*standardBasis,scale=scale,color=\"k\")\n",
    "plt.quiver(*origin,*altBasis,scale=scale,color=\"g\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 2.20"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1,  1],\n",
       "       [-1,  1]])"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([[2],\n",
       "       [3]])"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vec = lambda b: np.dot(b,np.vstack([2,3]))\n",
    "altBasis = np.vstack([[1,1],[-1,1]])\n",
    "altBasis\n",
    "vec(standardBasis)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Figure 2.9"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2],\n",
       "       [3]])"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([[5],\n",
       "       [1]])"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vec(standardBasis)\n",
    "vec(altBasis)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.axis([-scale/2,scale/2,-scale/2,scale/2])\n",
    "plt.quiver(*origin,*standardBasis, scale = scale, color =\"r\")\n",
    "plt.quiver(*origin,*altBasis, scale = scale,color=\"g\")\n",
    "plt.quiver(*origin, *vec(standardBasis), width=.01,scale=scale,color=\"k\")\n",
    "plt.quiver(*origin, *vec(altBasis), width=.01, scale=scale,color=\"k\");\n",
    "plt.quiver(*origin, *np.dot(altBasis,np.vstack([-1/2,5/2])), width=.007, scale=scale, color=\"gold\")\n",
    "plt.legend([\"standard basis\",\"alt basis\",\"vec(standard)\",\"vec(alt)\",\"vec(standard) w.r.t. alt.\"], loc = 3);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Whereas the same vector might be mapped to a new location, we could still find the same initial vector using the alternative basis, with new coordinates with respect to the alternative basis. \n",
    "\n",
    "To find the new coordinates we could consider that the previous basis was transformed to a new location, then apply that transformation to the new position of our initial vector, to find the initial coordiantes with respect to the new basis. \n",
    "\n",
    "Assume there exists a transformation matrix, `tMat`, such that $TU = V$. \n",
    "$$\n",
    "TUU^{-1} = VU^{-1}, \\\\\n",
    "\\therefore T = VU^{-1} \n",
    "$$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.,  1.],\n",
       "       [-1.,  1.]])"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([[2.],\n",
       "       [3.]])"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([[2.],\n",
       "       [3.]])"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tMat = np.dot(altBasis , npl.inv(standardBasis))\n",
    "givenAlt = np.dot(altBasis,np.vstack([-1/2,5/2]))\n",
    "undoT = np.dot(npl.inv(tMat), vec(altBasis))\n",
    "tMat\n",
    "givenAlt\n",
    "undoT"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.axis([-scale/2,scale/2,-scale/2,scale/2])\n",
    "plt.quiver(*origin,*standardBasis, scale = scale, color =\"r\")\n",
    "plt.quiver(*origin,*altBasis, scale = scale,color=\"g\")\n",
    "plt.quiver(*origin, *vec(standardBasis), width=.01,scale=scale,color=\"k\")\n",
    "plt.quiver(*origin, *vec(altBasis), width=.01, scale=scale,color=\"k\");\n",
    "plt.quiver(*origin, *givenAlt, width=.007, scale=scale, color=\"gold\")\n",
    "plt.quiver(*origin, *undoT, width=.003, scale=scale, color=\"cyan\")\n",
    "plt.legend([\"standard basis\",\"alt basis\",\"vec(standard)\",\"vec(alt)\",\"givenAlt\", \"undoT\"], loc = 3);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 2.21 (Transformation Matrix)\n",
    "*Book provides example for formatting a transformation matrix given a set of homomorphisms.*\n",
    "### Example 2.22 (Linear Transformations of Vectors)\n",
    "#### Figure 2.10 \n",
    "Three examples of linear transformations of the vectors shown as dots in (a); (b) Rotation by $45^{\\circ}$; (c) Stretching of the horizontal coordinates by 2; (d) Combination of reflection, rotation and stretching."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-1.        , -1.        ],\n",
       "       [-1.        , -0.89473684]])"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([[ 0.70710678, -0.70710678],\n",
       "       [ 0.70710678,  0.70710678]])"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([[2, 0],\n",
       "       [0, 1]])"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([[ 1.5, -0.5],\n",
       "       [ 0.5, -0.5]])"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "original = np.vstack([[i,j] for i in np.linspace(-1,1,20) for j in np.linspace(-1,1,20)])\n",
    "# There might be some alternate trick doing something like np.meshgrid but this will do.\n",
    "A1 = lambda theta: np.vstack([[np.cos(theta), -np.sin(theta)],\n",
    "                              [np.sin(theta),np.cos(theta)]])\n",
    "A2 = np.vstack([[2,0],\n",
    "                [0,1]])\n",
    "A3 = np.vstack([[3,-1],\n",
    "                [1,-1]])*(1/2)\n",
    "original[:2]\n",
    "A1(np.pi/4)\n",
    "A2\n",
    "A3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-1.11022302e-16, -1.41421356e+00],\n",
       "       [-7.44322928e-02, -1.33978127e+00]])"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([[-2.        , -1.        ],\n",
       "       [-2.        , -0.89473684]])"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([[-1.        ,  0.        ],\n",
       "       [-1.05263158, -0.05263158]])"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "colors = np.vstack([[i,0,j] for i in np.linspace(0,1,20) for j in np.linspace(1,0,20)])\n",
    "originalA1 = np.dot(A1(np.pi/4), original.T).T \n",
    "\n",
    "# Order of dot product matters here, the transformation matrix is applied to the column wise data,\n",
    "# if the original is dotted first transformations aren't applied correctly:\n",
    "# A is rotated CCW instead of CW, and D is skewed wrt to the y axis rather than x axis.\n",
    "\n",
    "originalA2 = np.dot(A2, original.T).T\n",
    "originalA3 = np.dot(A3, original.T).T \n",
    "originalA1[:2]\n",
    "originalA2[:2]\n",
    "originalA3[:2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,a = plt.subplots(2,2, figsize=(10,10))\n",
    "plt.setp(a, xlim=(-scale/4,scale/4), ylim=(-scale/4,scale/4))\n",
    "a[0][0].scatter(original[:,0],original[:,1], c = colors)\n",
    "a[0][0].set_title(\"(a) Original data.\")\n",
    "\n",
    "a[0][1].scatter(originalA1[:,0], originalA1[:,1], c = colors)\n",
    "a[0][1].set_title(r\"(b) Rotation by $45^{\\circ}$.\")\n",
    "\n",
    "a[1][0].scatter(originalA2[:,0], originalA2[:,1], c = colors)\n",
    "a[1][0].set_title(\"(c) Stretch along the horizontal axis.\")\n",
    "\n",
    "a[1][1].scatter(originalA3[:,0], originalA3[:,1], c = colors)\n",
    "a[1][1].set_title(\"(d) General linear mapping. Reflect, rotate, stretch.\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 2.23 (Basis Change)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2, 1],\n",
       "       [1, 2]])"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([[ 1,  1],\n",
       "       [ 1, -1]])"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([[1, 0],\n",
       "       [0, 1]])"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = np.vstack([[2,1],[1,2]]) # transformation matrix wrt standard basis\n",
    "B = np.vstack([[1,1],[1,-1]]) # given a new basis, what is the new transformation matrix?\n",
    "A\n",
    "B\n",
    "standardBasis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1,  1],\n",
       "       [ 1, -1]])"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([[ 1.5,  0.5],\n",
       "       [ 1.5, -0.5]])"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([[3., 0.],\n",
       "       [0., 1.]])"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T = np.dot(A,npl.inv(B)) #the transformation from A to B can be found as the dot product between A and inv(B)\n",
    "Atilde = np.dot(B,T) #we then apply the transformation to B to reveal Atilde\n",
    "B\n",
    "T\n",
    "Atilde"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Figure 2.11\n",
    "*Book shows the general relationship between vector spaces, and a set of transformations and their bases.*\n",
    "### Example 2.24 (Basis Change)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [],
   "source": [
    "Aphi = np.vstack([[1,2,0],[-1,1,3],[3,7,1],[-1,2,4]])\n",
    "B = np.eye(3)\n",
    "C = np.eye(4)\n",
    "#These are given new bases, and we seek to find the new transformation matrix based on these new bases.\n",
    "S = np.vstack([[1,0,1],[1,1,0],[0,1,1]]) #2.120 \n",
    "T = np.vstack([[1,1,0,1],[1,0,1,0],[0,1,1,0],[0,0,0,1]]) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-4., -4., -2.],\n",
       "       [ 6.,  0.,  0.],\n",
       "       [ 4.,  8.,  4.],\n",
       "       [ 1.,  6.,  3.]])"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dot(npl.inv(T),np.dot(Aphi,S)) # Using same method as above."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Figure 2.12 \n",
    "*Book provides the visualization for the relationship between Kernel and Image of a linear mapping.*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 2.25 (Image and Kernel of a Linear Mapping)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The image of a linear mapping, or function is the set of vectors returned from applying that function to a vector space, or the subspace returned by applying a function to a vector space. The kernel of a function is the set of vectors in that subspace, that return zero, when the function is applied to them. **I.e.** When a function is applied, we ask for image: What vectors are made the subspace? and for kernel: What vectors are sent to 0? \n",
    "\n",
    "*Recall Span:* Given two or more vectors, it is useful to know over what vector space any linear combination of the vectors could yield, which is called the span of these vectors.\n",
    "\n",
    "In order to find the image we're solving for, we're looking for the set of vectors that are sent to the subspace by our linear mapping. So we simply say the image is the span of `phi`. In order to find the kernel we're solving for the set of vectors in a subspace that are sent to 0. I.e. Ax = 0, to do so we find the basis of the `rref` of our matrix, or the span of the columns that form a basis of our reduced echelon form, are our kernel.\n",
    "\n",
    "```python\n",
    "'''\n",
    "Image = span(phi)\n",
    "Kernel = span(basis(rref(phi)))\n",
    "'''\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1 & 2 & -1 & 0\\\\1 & 0 & 0 & 1\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[1, 2, -1, 0],\n",
       "[1, 0,  0, 1]])"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1.0 & 0.0 & 0.0 & 1.0\\\\0.0 & 1.0 & -0.5 & -0.5\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[1.0, 0.0,  0.0,  1.0],\n",
       "[0.0, 1.0, -0.5, -0.5]])"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Phi = Matrix([[1,2,-1,0],[1,0,0,1]])\n",
    "Phi\n",
    "PhiReduced = np.array(Phi.rref()[0]).astype(np.float64)\n",
    "Matrix(PhiReduced)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1. ,  0. ,  0. ,  1. ],\n",
       "       [ 0. ,  1. , -0.5, -0.5],\n",
       "       [ 0. ,  0. , -1. ,  0. ],\n",
       "       [ 0. ,  0. ,  0. , -1. ]])"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#minus-1 trick\n",
    "PhiReduced = np.insert(PhiReduced,2,np.array([0,0,-1,0]),0)\n",
    "PhiReduced = np.insert(PhiReduced,3,np.array([0,0,0,-1]),0)\n",
    "PhiReduced"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0. , -1. ],\n",
       "       [ 0.5,  0.5],\n",
       "       [ 1. , -0. ],\n",
       "       [-0. ,  1. ]])"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "basisPhiR = PhiReduced[:,2:4]*-1\n",
    "basisPhiR"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We cannot visualize the image of the above as it is in $\\mathbb{R}^4$, but for the kernel, which is in $\\mathbb{R}^2$, we can, this is because the image is the span of the columns (size 4), and the kernel is a span of the rows (size 2). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [],
   "source": [
    "import random\n",
    "plt.rcParams[ \"figure.figsize\" ] = (10,10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [],
   "source": [
    "def span(vecs,n,ray=True):\n",
    "    fig = plt.figure()\n",
    "    ax = fig.gca(projection='3d')\n",
    "    ax.set_xlim3d(-scale/2,scale/2)\n",
    "    ax.set_ylim3d(scale/2,-scale/2)\n",
    "    ax.set_zlim3d(-scale/2,scale/2)\n",
    "\n",
    "    # If we were to iterate a scalar operation on a set of vectors n amount of times.\n",
    "    if ray:\n",
    "        for i in list(range(n)): \n",
    "            # A scalar operation on each vector in our set with a random value\n",
    "            fin = np.vstack([vecs[:,i]*random.uniform(-scale/2,scale/2) for i in\n",
    "                                         list(range(np.shape(vecs)[1]))])\n",
    "            # Summing set of vectors row-wise\n",
    "            vec = np.array([sum(fin[:,i]) for i in list(range(np.shape(fin)[1]))])\n",
    "            ax.quiver(*origin,*vec,color = \"gold\", linewidths = .5,arrow_length_ratio = .05)\n",
    "\n",
    "    for i in list(range(np.shape(vecs)[1])): \n",
    "        v = np.array(vecs[:,i])\n",
    "        ax.quiver(*origin, *v, color = \"k\", linewidths = 3,arrow_length_ratio = .05)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "span(basisPhiR,500)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The above is a visualization of the kernel (vectors sent to 0), of the linear combination matrix \n",
    "$$\n",
    "\\begin{bmatrix} \n",
    "1 & 2 & -1 & 0\\\\\n",
    "1 & 0 & 0 & 1\\end{bmatrix},\n",
    "$$\n",
    "which is the span of the basis of the `rref` above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0.0 & -1.0\\\\0.5 & 0.5\\\\1.0 & 0.0\\\\0.0 & 1.0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[0.0, -1.0],\n",
       "[0.5,  0.5],\n",
       "[1.0,  0.0],\n",
       "[0.0,  1.0]])"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Matrix(basisPhiR)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.8 Affine Spaces\n",
    "*Preserving parallel relationships. A point may be offset from $(0,0)$, and affine to $(0,0)$ by a scaling along some direction.*\n",
    "### Example 2.26 (Affine Subspaces)\n",
    "*Examples of affine subspaces are points, lines, an planes in $\\mathbb{R}^3$, which do not (necessarily) go through the origin.*\n",
    "#### Figure 2.13 \n",
    "*A line is defined by a support point $x_0$ and a vector $x_1$, with the equation $L = x_0 + \\lambda x_1$. We can intuit if the value of $\\lambda$ is 0 or 1, we have a point either at $x_0$ or $\\lambda x_1$* "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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/5ZOAc26Bc+56fPPsHmFyqstqYGo+83e2pLtzZj+L3HFiZofiC+N/8lxWSjwwORl4JVSIlfhCt/lgDVcaJ8Z+8wwwwiJ3WqX5vknbq4nOxI9bjJfLYfgrqZx3TwI4597BDwxdy5btmGvdOwLrY83o9e7IK5AF+ErqpNj0+P5K52X8enRNTQiteVU0vNLJdKWbr2fwXW6vpCkv8/P4/eYyHeqlo0hzXASFKuMpK/CDjB0w2XLc9RZMAA43sxPwrT0TIt+9hT/5V6U7diKB3jP4i91M2zzTPinkfo+K1ysj8SfSVB2Hc+5F/Jide/Ddr+PzTdw597lz7gF8wJ46Fqfjt/upqfnCUIJTKcyJs9H1mHNuLn6s2unhb0osSO9I/aAon3qimsj5IjgqTb53AT5Mk+/ZeSwjmsdinH9zlZ3pwImxYSLxJy6knusVPa4PYcvzTbP5N77V74fAC+FcOBs/JvMK4E3nXD69DE3WmA17Ej5avtU593L0CzN7AT+Y7kzgH03I1z/xlea9ZnY3sCf+xFjsBxROwXdrTTGzXwBz8MHSPkAH59yV6X5kZrfjr05ewt8QMAw/CPkHYZb/4CvdX5vZGPyVxmh85R63GHjK/GM4OuDvzHk1tNLks6yUY8zsOvx4gZH4g/gk8JWdmU3HtwatwB+EPwzpRU8wt+CvaJ8PaS3AVw6dnXM3NHZ7RexjZqfGpn3qnHvWzK7BD75MW2bDiemrwP3Oualpvn8IODfNVXTq+8fxLQMz8Qfiqfjj47kGrPvlZvYr/F2Oh+DviCo459xGM7sRuNHMPgVewAcUg8IsmzL+2A9AvQgfPPwCP+7jenwF9GgD87HOzN7HBwav46/aX2tAEmPxx8LTZnYPvhVsR3zZHJ9uP0asAa4LAdjH+PqhPXBrhrwWqoxH01xi/tb25/HH6FfSla2Ip/FjbW4H3g9jtFJpbTKzK4A/haDub/igagC+XJ8a0h6HP0E9Z2Y34VvI9sUPbr8HH9ABXGhmE/AtRLMp4H6P2TPUQY/ix9ScB3w31jUFcDe+S3hatOUiHTO7EN/SMQm/b3fFtyTdB+Cce8PMHgR+G7bVu/iHd+9O+taghmpqPfYQ/k7b7iFf8bR/Z2ZX4YPjY/EtMrk8DvzGzH6E3/8j8efFqPvwLflTzT/qYh6+K/sAYJFz7pY8lgPFO//mKju/wG+jP4d87BXmiXoJfzPIneYfHdIHX698lGvh4fidG5Z9ZZi2KcQxx+FvHigO18DR/fjBz29n+f73+FaJSvK8OzBDOmfj7/ZYg9/YB8Z/R9PvmnwkNs9Q6t/GW4mv/FKDEFPjG7Ld1XUO/uS4FF/xvgacF5tnf/wBtRp/8j80zfpNBR7BH1wfhm3xN6BvvsuKrNOI8NvV+CuOi2P52QV/ANaEZY3OsH374SuaZSGt/wJnNGV7RfZPur+pkX3tsvz+1DD/IRm+T90hdnqG7/8fvln/c/zg/pfxTfMNWffR+BN3Df5CZNc05S6+j8eT5U6cLL8z/GMjPg35vR9/EnLAVjm29b5hX6/GV64PELurK768LGkdHcpcbVh2FZmPwTrrGqbtji/jS/Hl+118oJLx8TapcokfDzILfzX8XyJ3amXYZk0u4+nWLcz/Ib6ct8+xvf4v/P7nGb4/Bh/Y1eAvzGbhxy+2jczzRfzYqZVsKavDI99fgb8DcwMwP9/9nmm/Zchnat5R+N6RlaEsjiPNo0fCtnfA+XmkfTA+aP04lKv38Sflysg8nfBdlZ+E/T8DGBFLZyr16/h0+3soBaj306xrLZE7CsN3Ffiur8Vh/z6KP7fFy1S83miHD6YXhXJ5K74bu05dgQ/+bsXXQ+vwdf1jwKFZ8ptu/fM5/zZq+zak7OAD8HfDtvw3/rxZ565JfFfq6yGvr+GD23p5y7DufyB23sA3Yjgid4imq78o4F2TFhKQMmX+IY//AgY5515PODvSjMzsLvxYieYamybSKGZ2MXADsIOL3LkpIsUfcyUiBWD+Bb2n4x9IvAnfknIu9bukRRJj/k0Lu+Hv7B6vIEykPgViIi1TDf7OrEvwDyf8AB+E3ZRkpkRixuLfCPIs/m5CEYlR16SIiIhIQhr90m8RERERaRoFYiIiIiIJUSDWTMysl5mNDYNVo9OHmpkLg62lxJnZbmE/bpV0XorFzKaa2SORz2PNLNeT7tOl48zskizftw9p79PYvMbSS+SYM7PxZpbzgcW5tkcjl12wdTOz+WZ2TgGyVZLM7AIzK9hbP8xsr7Dth0amZd2GZlYVfnN8ofIRS390ND+R6QUve6XIzM4J69ol6bw0hAKx5tML+DH5PeFXStdu+P3YagKxImqP37YFCcTQMSfZXUByr18rltH453ZJC6JATIDNT6aXZmZmHXPPVT7LFUmayn7L1hr2X8kHYqGp95dm9kMzW2hmn5vZTeYda2ZzzGylmf3FzLaO/bZ/mL4izPOkme0S+f5ZM/tzmmX+0sw+NPPvuDKzDmZ2g5ktMLO1ZvZfMzs2S56r8K8OAfhXaCqN357a08weNrNVZjYvPPAwns5hIY+rzWyJmd1pkXfFZVn+aWY2O+R1gZldZ/6lranvU823B4RuqDX4J8tjZteH364ys2ozu9/Mtouln9on/xvmWWZmE+Ldd2b2RTN70cxqw3461sxmmNn4pqynmZ0b1i2+vD3Deg2PTDspLLPWzBaF/dguTT6fNLPlYb3/Y2ZHhSb+J8Ns74e050d+t4+ZPRPyvSxsq96R71PdEKPM7D4zWx5JL75OqXnPMrM/hfK62Mx+HJtv97CtF4TlzjGzyy3y8mrb0l01wsyeMLNVwG/Dd1eY2XTzx9En8WMiX2a2jZndHtKoDfv5wAYmszL8e2/qGAnHDmbW08z+GMrD6lBOB2fJTxUJHnPht181szfD9vi3mcXf9xqf/zgzmxL28woze8nMjk4zX9rymSXdM8xsnZl9O598Z0nnRDN7xcxqQvl+2cILqi1DF5vFumktdGub2aFm9mrYNrPM7LDY71J1yphwnK4Kx1P32Hz9LUudHuZxZvY9M/uV+VeAzTazqcCXgG9Eyto5kd+cH46ltWb2gZmNTrM9Lg7HXY2ZPUnjXr6e0i3TcW5b6rHDY8vvErbLZekSNF839QB+HFnHoZFZKszsZ2b2aVjm78ysMpbGTubrl6XhGJhsZl/ItiK25Xyyv5k9b2ZrzOxtMzs5Nt98869eSvfbLuFztrortV9vDflbbma/MbP4y9Dj+WvQ+TsRDX0Uf7H/8K9VSL2m4Sv4d1k6/DvhXsG/c2sU/rUPt8VeUTEP/+6104FT8K9B+AjYJsxzEf51H50jvzP8M5mir3J4Cv9Kiovwr3S5C//6kH0y5LkS/+wcB1wMHAQcFHvdwzvA1fj36t0Tph0QSeNQ/Ks7HsK/suF/Qt6zvrYh5M8Bfwzba3RIJ7ptzgnzvId/h9gwYN/w3T34d4Uejn9t0DRgLlAR2ycfhu1yLL7JfxXw+8g8nfAvcJ2Jf7nrmWFfLMY/2LHR64l/jcda4NzY9J/gX3lSET6fBmzEv3br6LD/lsf27e74gGAGcEbYH1cC38S/X+6KsK1ODvsxtZ22DWlNw3d3fB1fTl8jvOaGLa+8WAj8LqR9RIZ1Ss37Ef4VPyOA6/APa/1OZL7h+FeBnBDK0uX41zJdGZlnaEirGv8apCMIr/DAHzffCPOciH9VzidEXsVC7PUgxF5bgi/fr+KPr7Px5Wxi2I7bRear85qWNOs8LMzz07BtDyK8xgb/OpNF+IfUnoB/5+dKYJcSPObG41/RMg9fF43EB4UL8O8mTLs98M+Auyzs66Pwr7DZSOR1NGQpn7F1S70+5hz8q23OyZbnPOrdnUM6N4bycyz+OWAnx8pr1tdYhbKzGv+aogvCvpyapqzMD9v62TDPBfjj6+GG1OmR7bww7MevhLzvAbyBf3VSqqxtG+b/f8B6/PF2FP4dpGtj++qkkO4fwv76Wdi/DhjagO2a2m65jvNpROrJMO3ckK+eGdLeN2yzuyLr2C2yTT4M+2dEWOcNwOjI77cJ88zE153H44/DBUDHLOt0Tkh/Hv58cgz+1U0bgL1j+/iXGX6bek3QUDLXXant9mhYxvfD9rgxU3phWoPO30n8JZ6BPArufPy7pqKBwH/ChuwfmXYD8Enk87fDPAMi0/rgK5crw+dtwzzR9wUeHHbk4PB5ePh8eCxfzxGpJNLkey/SHKSRgvaTyLR2+Ir8+si054F/xX57BLF3gqVZ7ktpfjcaX8H3iRXW7+bY9hX4lzA7Iu/xC/vkPeq+/+5X+BfLpj5/J2zrHSPTUu97HF+A9ZwITIpNewv4bfh/KqC+NzbPN/HvJOsRPj+IP+jTVjT4ysgBVbHp1+MrvW5p1u/M8LkqfH48j3Kemvfvsel34iufNml+Y/iHMv8ImJemjN2Sx/7tiD8pnh2ZPpXsgdh5Yd/uGpnWNpSJaKWYKxDrQuy9cWH6V4gdc/iH1n4K3F6Cx9x46r+vrh++bvl2PtsD3zvRFv+y6Xsi03OVz9S67YWv89YSqc8a+4e/CFuSR3nNJxBzwFmx/b40tu3nh2nRE+gofIAyMHzOWadHtvPMNHmeQf3gphv+IvLHsek/wV8IpC7q/gP8Lc2x2dhALOtxDpwf8hXdHs+R+6LgM2BsmukOeC427S/AS5HPP8W/RD4a1G6Nv9D7TpZlnhPS/1GsPL8JTIjt43wDsXp1V5j+JpG6EN8ws5otjSvx9Bp1/i72X8l3TQZTnXMbI5/fxb/M9v3YtG0jzZQHAK865+alZnDOVeNfkH1Y+Pwp/iW4p0fSOR14zzmXal4/En9AvmBmbVN/wDNAxq6SPPw9kq/1+Kv1PgBm1gkfEP45tsx/46/cvpQuQTOrAPYDHo599RD+wDg4Nv3pNGkcY76b6XN8pVcdvtotNuu/nHMbIp/nAr0i239/4BXn3EeR9fwPvvUltaxGrWdknYabWc+Q1j4hjw9F8rtTmrT/CXTAn7jAn2gfcs6tybKsdA7AV6abX9kS1m8+oXxF1NvOWTwe+/wYsANbykYHMxtnZu/iT7qpK/n+Ful+zrRcMzvIfHfYEvz+XY0/Mcb3bzZH4luj349sV/CtGU05JlIOAD51zj2bmuCcq8Ff2ca3bUMU/JiLWOycezGS/gf4bXRAph+YWR/z3a8f4ffFevwVe3Rf5Fs+L8NfDJ3hnJuQY958zAa6h/wdbWadm5je5nLtnFsFTKH+tpkSvkt5DH+xsX/4nLNOj8j3mDsYH+Q/nKae6A30CfXqvviLv6jH8lxGOlmPcyC1D78GYGY749fx3iYs8++xz3MjywN/XE8BVkS2w0p8Oc7nuI7u40347ZWx/OeQaf9NDGmnPIa/mMx013Bznb8LqqUEYstjn9dlmGb4O7HA999/Qn2f4JtgUyYAx5hZN/PjbL7GlpM5QE9gO3wlGf0bC/Rt6IpEpMt/asD81vjWit/HlrkWfyWfabk9w/fx9U593ibDdADMbH/gCXzw9T/4Suqg8HV8MH+u7b8dvsUhLjqtsetJyOd6fDcQ+AD6I/yJE/y2AN/1Fk07Fbyn0u6B78ZoqHzLFxnmy2Rxhs+p8Si/wDfJ34HvctkfuDZ8F99H8f27E74yNuBCfFfc/mEZDblZoye+XMSPiXNp2jGR0pBt2xDNccylxPdbalracUShrnkCOAS4Bt9Nuz/wN+rui3zL5yn4i9F/5DFvTs65t/DdcQPwx9BnZvaAmW3biORWpQkk022bOtsw/GZVZL7mOOZS9cQc6u73f4XpffE9J23j+UvzuSGyHuchIP0z/pgC39KzCJjUhGVmK//gt8Xp1D+uh5HfcZ1unRo7ji7T/stVP8Y11/m7oMr5XZMLgT3TTO+NbwJPeRzf738SvitrB+oGYkvxJ/hi3va8HN+cOhZfCcZ9nOF3n+ELWa/Y9NQA8qWx6S72+WR8oHS6C+23ZtYvvyzXswhIN8gzWpE3dj1xzq0ys6fxFccd+DENf07lmy3regF+zENcKiBbQuMqi4XU387gt/Ur8ew2IN14mqnPqZPx14DfOOduSM1gZsdlSCu+3K/gx+6dFFqYCFeHDQ1uluK7eS5K893aBrzKEgYAACAASURBVKaVTrZtGy/DhdLoshiky28v/Ak+nV3wrSzHOOc2n1yt/h1i+ZbPUfh67EkzO6YRLbz1OOeeBp42P2D+OHyL22/wY9Vqw2zxgdLpylIXM+sYy1Mv6geYdbZh2BZdIvPlW6dD/sdc6nfHk/7k/xa+1XhDPH9pPjdEruMc/FimF8xsV/xYzPtiPUOFthR/cfDTNN+tTDMtrhe+vEY/R9enlvzKC2Tef/lst6gkzt8N1lJaxBrjZeBLZtY/NcHMdsRfgaZaTXDOLcO3Epwe/t5wzr0WSecZfES9yjk3I/6XZfnrwr8NfixEOEm+BHwh3TKdc2lPCuEgfYXQnB1xGn6sxbQci+4IrI8EM+Ar+MaYDgwO2xwAMzuALUFho9czYgJwuJmdgL9yj3bJvIU/AKsypJ2qMJ4BTrPMj+/ItB9fBkZY5I660KJYRaR8NcLJsc8j8ZVMqou4I5FgJ3SbnJFn2h3x5SDapXwaDb8gewYfSHyYZrvOzvXjiGzbtpeZDUlNCF2Hx5F92xb9mIvoZWaHRPK7E36YwH8yzJ8KuKL7sh++lTIqV/lMqcaPh9kVeMRidwY3hXPuc+fcA/iL1tSdoIvxF30DU/OFO9/iwx9STo7NdxT1t81RVvdBnCPxJ+RUPZtXnZ5FvAUIfJ24Btghw35fGerVWfiL9aiRNF6u45zQ1f0m/saSnfDj73JJt475egYf6M5Jsx3eyuP30X3cBr+9ovu4mkh5CTLe/ZvBSRa5Qxy/3dbgb9pIp7Hn76Iq5xax8cAPgL+Z2TX4wepj8a1Gt8fmfQhf2D8n3CobMQU/gHaKmf0Cf4XbDf8Qyg7OuSszLP9DfAH5Rhhvtb6BO3408IyZbQIewV+R7IQ/GV3lnHs7w+9+DEw2s3vxgckg/BXOnWE8RTZTgMvN7Ff4xywcgr8bsDHuxd+h9pSZjcOfeMbhW9yiffyNXU/w4whW4/fn+2GMFuDHKJjZFcCfzKwbvstnHT5g+ypwqnNudcjTdOA5M7sJf0W3L36g8j34gA7gQjObAKwOwcbN+BahyaFcdMEP4J+Nv6unsfY0s9tDGkPwA+O/GxkXMQX4ThgjthR/U0Rl2pTq+ye+++1eM7sbX+l+n/pdFrnchx84PdX87ejz8F1oB+Bv2Lgln0Scc+vM7H18oPE6/or5NefcZDN7AXjIzH6I3yffx5ehG7MkmdQxB75e+ZOZjQl5+AnhDuEM87+JPzHdFH7TFV8WP4rNl6t8buacm2dmR+IHIv+fmZ0ZjoMqfAvwuc65TPmpw8wuxAdVk/CtgbviL/DuC8vaZGYTgf81sw/wZeiKsO5xa4DrQpD1MX5ftgduTTPf02Z2I74V8Eb8jS5zw/fjyb9OT+dN/MXTCPx2fN85t8TMxgK3hkD4OXwDxW7AMOdcKrj4GfCYmf0BH5Aejm9hbqxcx3nK3fjtMM0592ae63icmU3Cd+u+5ZzLpzULfJ32deCfZvYbfFnsjV/XfzvnHszx+/PNbB0+KPoW/mLtzMj3jwO/MbMf4cv0SNK3cGbTFT+e787w22vwN2hlainP6/wd6sPDnXMNfpRPQbgSuGMg2x/p77QYT+TOHJfmbokwbQD+zpCV+EL5FJE7vSLzdcWf0B3+ijj+fSW+QnwXfzJP9dUflyPvo4C3w2+cq3tXyF6xeacSuyMGODAsZwVQgx9ceTORRw1kWO7p+IBgHb6yv466dzjW21aR70bjb1euwY832ZX6t92n2yfptv/ewIv4q/638AHQ28CvCrGe4bf/F5b78wzfH4O/G64mpD8LP6Yquj2+iO+OWhn+XgaGR76/At9tvQF/k0hq+r744GY1/kT0ANA78n0Vae4sy5DP1Lyj8HfKrcQHreMAi8zXG1+hrcB3pdyAr/TS3XlU704/fBfHe/iT3kth29fZn/GySOyuyTCtO/5EuiBSzh6j7qMXMt4lGJnnaPwjP2qJ3J2K78K+D/9YmjX4GwH2z2M7Fv2YI9RH+BPL2/jy/kKa5cWPo/3xLQZr8DcOnEP6ui1j+Uy3bmx5jMHd+PGAe4R5js21/SJpHIy/0Pk47Jv38eMTK2NlcWLYVh/ghwHUyT9bAqUv44+9tcB/idyFHalTbgrzfxK2/YPAVrH5ctbpmcpd+O0/8BfcjsjduvgA5JWwL5aFbfy92O8vwZfz1WF/pB4VNLQB27WKPI7zyPy7hPnPzzP9L+GP65po3tJtE9If1zvgL6I/CftqPr6O3TPLMs8J6R+AL/e1+HPlKbH52uGPpUVhG98ayky+dZcDvodvLFkW9uPvYmXyHOqfh3Kev/Hldn6mdWzuPwuZEGl2oUvhbeAC51xT7v4pO5FWixOcc08lmxspJ2Z2Lr51eldXv8WluZc9Fh8A9Mwx33x8UPz9YuSrpTD/0OEb8F2nK3LNnwTzD8a9F+jq6t71WujlOOBS51y816rFK+euSUmYmV2Jv6L+AN/FcyX+6q8pXXci0jCH4FuhixqESeOFC7Pd8M8IHF+qQZgUhgIxaU4OP2ZtB3wz9/PA91WpiBSPc+5bSedBGmws/k0Rz+LfaCBlTF2TIiIiIgkp58dXiIiIiJS0RLome/bs6aqqqpJYtIiIiEiDvPLKK5855xrzZomcEgnEqqqqmDGjZJ6lJiIiIpJReF5es1DXpIiIiEhCFIiJiIiIJESBmIiIiEhC9BwxERGRErR+/Xqqq6upra1NOiutRocOHejTpw/t2rUr2jIViImIiJSg6upqunbtSlVVFWaWdHbKnnOOJUuWUF1dTf/+/Yu2XHVNioiIlKDa2lp69OihIKxIzIwePXoUvQVSgZiIiEiJUhBWXElsbwViIiIiIglRICYiIiKSEAViIiIiUhDOOQDGjh1b53PK7Nmz6devH3/4wx+KnbWSpbsmRUREWoBx48YVNL0f//jHBU0P4P777+fjjz+mtraWG264gR122IGvf/3rm78fNGgQEyZM4Hvf+x4XXXRRwZffEqlFTERERDIaNmwYU6ZMAeDqq6/msssuyzjv17/+dfr27csNN9zATjvtVCcIS+nVqxdz5sxptvy2NArEREREJKNx48Zx3XXXcf/99zNz5kxuueWWjPM+8MADLFiwgNGjR/Phhx/ywAMP1Jvnhz/8IWvXruWDD5rtPdotiromRUREJKMhQ4bgnOPmm29m6tSpVFRUMG/ePK677jo+//xzHnnkkc3znnnmmZgZY8eOZfTo0fXGiE2aNImamhqOO+445syZQ79+/Yq9OiVHLWIiIiKS0ezZs1m4cCGVlZV07doVgAEDBnD33XfXmzf1HK7UYP3oc7lqa2sZPXo0v//97xk0aBCvv/5682e+BVAgJiIiImktXLiQUaNGMXHiRDp37szkyZMbnda1117L2WefTVVVlQKxCAViIiIiUs/q1asZOXIkN910EwMHDmTMmDGbW7oa6q233mLKlClcfvnlAArEIizef1sMgwcPdjNmzCj6ckVERFqKN954g4EDByadjbSWLFnCVVddxZQpUzj//PO58sork85SwaTb7mb2inNucHMsT4P1RUREpEF69OjBbbfdlnQ2yoK6JkVEREQSokBMREREJCEKxEREREQSokBMREREJCEKxEREREQSokBMREREJCEKxEREREQSokBMREREJCF6oKuIiEgLEH2BdiEk8WYdqU8tYiIiIpLRsGHDmDJlCgBXX301l112WcI5Ki9qERMREZGMxo0bxzXXXMPixYuZOXMmTzzxRNJZKitqERMREZGMhgwZgnOOm2++mQkTJlBRUcG8efM477zzOPXUU5POXounQExEREQymj17NgsXLqSyspKuXbsCMGDAAO6+++6Ec1YeFIiJiIhIWgsXLmTUqFFMnDiRzp07M3ny5KSzVHYUiImIiEg9q1evZuTIkdx0000MHDiQMWPGMHbs2KSzVXYUiImIiLQAzrmC/uXSqVMnpk2bxlFHHQX4sWLTpk0DYMmSJXz7299m5syZ/PznP2/W9S53umtSREREGqRHjx7cdtttSWejLKhFTERERCQhCsREREREEqJATERERCQhCsREREREEqJATERERCQhCsREREREEqJATERERCQhCsREREREEqIHuoqIiLQAN+61oKDp/b/X+xY0PWkctYiJiIhIRsOGDWPKlCkAXH311Vx22WUJ56i8qEVMREREMho3bhzXXHMNixcvZubMmTzxxBNJZ6msKBATERGRjIYMGYJzjptvvpmpU6dSUVFBTU0NF198Me3bt2fo0KGMGjUq6Wy2WOqaFBERkYxmz57NwoULqayspGvXrgA89thjnHrqqdx5551qIWuiggViZlZhZjPN7KlCpSkiIiLJWbhwIaNGjWLixIl07tyZyZMnA1BdXU3fvn6wf0VFRZJZbPEK2SL2XeCNAqYnIiIiCVm9ejUjR47kpptuYuDAgYwZM4axY8cC0KdPH6qrqwHYtGlTgrls+QoyRszM+gDHAdcB3ytEmiIiIrJFsR830alTJ6ZNm7b585AhQzZ/HjlyJJdccglPP/00J5xwQlHzVW4KNVj/V8BooGuB0hMREZES1blzZ+69996ks1EWmtw1aWbHA4udc6/kmO8CM5thZjM+/fTTpi5WREREpMUrxBixQ4ETzWw+MAE4wsz+Lz6Tc+4O59xg59zgbbfdtgCLFREREWnZmhyIOeeudM71cc5VAWcA/3TOfb3JORMREREpc3qOmIiIiEhCCvpkfefcVGBqIdMUERERKVdqERMRERFJiAIxERERkYQoEBMRERFJSEHHiImIiEgzecAKm95ZrrDpSaOoRUxERETqGTNmDLfeeuvmz1dddRW//vWvE8xReVIgJiIiIvWcd955/PGPfwT8i70nTJjAqFGjEs5V+VHXpIiIiNRTVVVFjx49mDlzJp988gn77rsvPXr0SDpbZUeBmIiIiKR1/vnnM378eBYtWsQ3v/nNpLNTltQ1KSIiImmdfPLJTJo0ienTpzNixIiks1OW1CImIiIiabVv355hw4ax1VZbUVFRkXR2ypICMRERkZYggcdNbNq0iZdeeomHH3646MtuLdQ1KSIiIvXMnTuXXXbZheHDh7PrrrsmnZ2ypRYxERERqWePPfZg3rx5SWej7KlFTERERCQhCsREREREEqJATERERCQhCsREREREEqJATERERCQhCsREREREEqJATERERDK6/fbb+c53vpN0NjKaPXs2/fr14w9/+EPSWWkUBWIiIiKS0WuvvcagQYMSW/7UqVM555xzMn4/aNAgJkyYwH333Ve8TBWQAjERERHJaPbs2U0OxIYNG8aUKVMAuPrqq7nssssKkbXNevXqxZw5c4q6zELRk/VFREQko9dff5299tor7Xdf/vKXWblyZb3pv/zlLznyyCM3fx43bhzXXHMNixcvZubMmTzxxBMFzeMPf/hD1q5dywcffEC/fv2KssxCUSAmIiJSLtatg8mTYcQIaN++ycktWLCArl270r1797TfP//883mlM2TIEJxz3HzzzUydOpWKigpqamq4+OKLad++PUOHDmXUqFF1fnPggQeydu1aVq1axdKlS9lnn30A+MUvfsGIESM2zzdp0iRqamo47rjjmDNnzuZALN0y582bx3XXXcfnn3/OI4880phNUnDqmhQRESkXkyfDKaf4fwsg1/iwL3/5y+yzzz71/v7xj3/UmW/27NksXLiQyspKunbtCsBjjz3Gqaeeyp133pm2terll19m1qxZ3HXXXZx44onMmjWLWbNm1QnCamtrGT16NL///e8ZNGgQr7/+etZlDhgwgLvvvrtJ26TQFIiJiIiUixEj4NFH/b8FkGt82PPPP785QIr+RbslFy5cyKhRo5g4cSKdO3dmcggSq6ur6du3LwAVFRWNyt+1117L2WefTVVVVZ1ALNMyS5ECMRERkXLRvj2ccEJBuiXBB2J33HEHVVVVVFVVcfDBBzfo96tXr2bkyJHcdNNNDBw4kDFjxjB27FgA+vTpQ3V1NQCbNm1qcN7eeustpkyZwuWXXw6wORDLtsxSZM65oi908ODBbsaMGUVfroiISEvxxhtvMHDgwKSz0Wxqamq45JJL6NChA4cddli9MWLNYcmSJVx11VVMmTKF888/nyuvvLLePOm2u5m94pwb3Bx50mB9ERERKbrOnTtz7733FnWZPXr04LbbbivqMnNR16SIiIhIQhSIiYiIiCREgZiIiIhIQhSIiYiIlKgkbqhrzZLY3grERERESlCHDh1YsmSJgrEicc6xZMkSOnToUNTl6q5JERGREpR6ztann36adFZajQ4dOtCnT5+iLlOBmIiISAlq164d/fv3Tzob0szUNSkiIiKSEAViIiIiIglRICYiIiKSEAViIiIiIglRICYiIiKSEAViIiIiIglRICYiIiKSEAViIiIiIglRICYiIiKSEAViIiIiIglRICYiIiKSEAViIiIiIglRICYiIiKSEAViIiIiIglRICYiIiKSEAViIiIiIglRICYiIiKSEAViIiIiIglRICYiIiKSEAViIiIiIglRICYiIiKSEAViIiIiIglRICYiIiKSEAViIiIiIglRICYiIiKSEAViIiIiIglRICYiIiKSEAViIiIiIglRICYiIiKSEAViIiIiIglRICYiIiKSEAViIiIiIglRICYiIiKSEAViIiIiIglRICYiIiKSEAViIiIiIglRICYiIiKSEAViIiIiIglRICYiIiKSEAViIiIiIglRICYiIiKSEAViIiIiIglRICYiIiKSEAViIiIiIglRICYiIiKSEAViIiIiIglRICYiIiKSEAViIiIiIglRICYiIiKSEAViIiIiIglRICYiIiKSEAViIiIiIglRICYiIiKSEAViIiIiIglRICYiIiKSEAViIiIiIglRICYiIiKSEAViIiIiIglRICYiIiKSEAViIiIiIglRICYiIiKSEAViIiIiIglRICYiIiKSEAViIiIiIglpciBmZn3N7F9m9oaZzTGz7xYiYyIiIiLlrm0B0tgAXOGce9XMugKvmNkU59zcAqQtIiIiUraa3CLmnFvonHs1/H8l8AawY1PTFRERESkFBtZcaRd0jJiZVQH7Ai+n+e4CM5thZjM+/fTTQi5WREREpDDWrYMnn/T/BltDt+ZaXMECMTPrAjwKXO6cWxH/3jl3h3NusHNu8LbbbluoxYqIiIg0Tpqgi8mT4ZRT/L/BMqgX1xRKQQIxM2uHD8Lud849Vog0RURERAoiXcAFaYMuRoyARx/1/wYOXHNlrRB3TRpwN/CGc+7mpmdJREREJIdMwVWerVxA2qCL9u3hhBP8v0VQiBaxQ4H/AY4ws1nh79gCpCsiIiLSsOAqz1YuoOhBVzrmXLO1tmU0ePBgN2PGjKIvV0RERErcunU+iBoxYkuA9OSTPrh69FEfOGWaL9v0JjCzV5xzgwuSWIyerC8iIiLF18RxWxlbs0qglashFIiJiIhI82ph47aKSYGYiIiIFE6+QVcJj9sqJgViIiIi0nDN1bXYyigQExEREa9MHgnRkigQExERaY3K+JEQLYkCMRERkXLX1HFbauVqNgrEREREyoUeCdHiKBATERFpiTRuqywoEBMRESllTW3lAgVdJUyBmIiISKlQK1ero0BMRESkOTX1kRBq5SprCsREREQKpTkeCaGAq6wpEBMREWkMPRJCCkCBmIiISDZ6JIQ0IwViIiIiKRosL0WmQExERFofPRJCSoQCMRERKW9q5ZISpkBMRERaHj0SQsqEAjEREUnOxrWw4HFY8VbmefRICCljCsRERKS4nIPPXobp34HHd4APHoSuu/nv9EgIaWXMOVf0hQ4ePNjNmDGj6MsVEZEE1XwA7/8fvH8fLHsbXgMO6gcn/hfad/fzPPmkD7oefdQHT+CDssmTfXClYEoSYGavOOcGN0fabZsjUREREQDWr4B3H4JHfg39Xt9y1nkN+BXwx0u3BGGQvUVLpAwpEBMRkcJItVwddSQsfc63fFU/DtPX+KDrcmC/MO8XgV+fC1+7tG4aCrqkldEYMRERyS7duK100x69HUZ+FX6yI0z9CnzwAGxc44Ouy/H/pvQ9Bi66S12N0uopEBMREa8hDzlNTXviIXjzFvjbvrD+MvjuJth9Wd3ft8W3hKX6YDruAAf/EUynIBEdBSIirVFTH3K65zoYuzesOQde/R4sm1U/4ErH2sAh90OHbQu3LiItmAIxEZFy1xwPOd3+EBhxaMO7FvccA72HNngVRMqVAjERkXLR1PcnNuR5Wx23hy/9Ck6cB1/4LrRpl/s3vQ6Hvcbkty4irYQCMRGRlqhU3p9Y2RMqOsCm9bnnO+R+aFPRtOWJlBkFYiIipayprVzQfE+Wr1kAzwyDub/IPe9Bf4ROOxZ2+SJlQIGYiEgS8n0kRBKtXPn46K8waV/49IXc8+5+Bex4bPPnSaQFUiAmItKcGvNIiCRbuXLZtB5m/RCePQ7WLqn7nbWFAefUndbjANj7Z0XLnkhLo0BMRKRQmtqilXQrVy7ZuiI79YUjn4Mv/XrLtHbd4NAHoaIE8i5SohSIiYg0RnM8EqKUgq64bF2ROxwPx8yCbQ+Gdl2hy85++oF3QZcBxc2nSAujQExEJJtiPhKiFOXqitz3l3D4E1C5zZbpW+8Nu1wIO32tuHkVaYEUiImIpLSkwfLFkE9X5MArwKzud/3Ogv1uKU4eRVo4BWIi0vqU8iMhSkW+XZHp7HQKtO3YvPkTKRMKxESkfLT0R0KUgsZ0RYpIoykQE5GWp9weCVEqGtsVKSKNpkBMREpbuT8SolQ0pStSRBpNgZiIlIbmGreloCs7dUWKJEqBmIgUn8ZtlQZ1RYokToGYiDSv5njwqTSduiJFSoICMREpjNb+4NOWQl2RIiVFgZiIZKdHQpQPdUWKlBwFYiLi6ZEQ5U1dkSIlSYGYSCvy9j9Ws3LRBj0SojVRV6RISVMgJlLOYgHXNlXtuPuERbx+0aM4PRKi/KkrUqTkKRATKRd5tHL13KUdu3+lE5OnHcBTA25n+sKDWV+7yc+r4Kq8qCtSpEVQICbSEjXhkRCHXNyNNh0rebPtkUz99RruPm4Rsx9bxaaNrogrIM1GXZEiLYoCMZFS1gyPhOi2fVv2PavL5s8rP9nIpGuWMX7kIt791xqcU0DWYqkrUqTFUSAmkoSEHwlx4PldqexW92S85L0NPH7pZzx49mKqX13bmLWSJOXsipyprkiREqRATKQ5legjITp2r+DA87ul/e6jmet48OzFPH7pp3z23vpGpS9FlHdXZI9k8iciWSkQEymUFvZIiP3O6kKX3hUZv3/3X7WMP3kRk8Ys9Y+8kNKjrkiRFk+BmEhDNXXcFpTEIyHadWjDYd9J3yqW4jbB7MdruOu4RTx783JqP99UlLxJHtQVKVIQ7733Hi+++CJz585l4cKFrFnjx8quXbuWSZMmcdNNNzXr8ts2a+oiLd26dT6wGjFiS4CUCrgefdQHTinZWrRK1J4ndmb6H1ey5L3sLV4b1jr+c89K/vvIKg46vxv7ntWFdh10HZeITevhtTHpW8GsLexzPez+PbWCieSpZ8+eTJgwgQ0bkmn5VyAmkpJv0JWrlasFadPWGHL5Vjx+6Wd5zb92hePZmz/n/RdqOenmnnTormCsqGoWwItnpm8F69QXDn1IrWAiGdTW1jJ58mTefPNNamtr8/5dmzbNW89ZEreqDx482M2YMaPoyxUB0gdc4Lsb40FXpnnLiHOOB89ezEcz12Wdb+t+bfnC0R35wohObPuFdphaXIrro7/CS2fXH5APvivy4PEakC9C4wOulG222YYTTjiBqqqqzdPM7BXn3OACZnMztYhJ+UgXNJV512IhmBlD/ncrHjx7cdb59vt6F/Y7s2uRciWbqStSJK3GBlxmRseOHdl7770ZMmQIHTp04C9/+Qvr169nyJAh9O7duxlzXZ8CMWl5MrVSpQuwyrxrsVD67FfJLsM68O6/Mldmz1y3HEDBWDGpK1KkoAFXJkcccQTdumW/eam5qGtSSlu6oCtdF2KmeVtB12KhfPbuesaPXITLcWPk8Ku2UjBWDOqKlFamGAFXYzVn16QCMSkNGrdVEiaNWcrsx2sA6LlrO3Y9oiPTbl9Rbz4FY81IXZFS5ko54MqybI0RkzKicVsl65CLu/HGX1ezYa1j96905KALfFN9PBhTN2UzUVeklJGWGHAlQYGYNK9W+EiIlqzb9m3Zb1QX/nPPSr5wdCfMjEMvUTBWFOqKlBK1YsUK1qxZw9Zbb037NL0QCriaRoGYFEZDBtCrlaukHXheNxa+to5t+rcDUDDW3NQVKSWuffv23HPPPXz++eeYGQ0d0qSAKzuNEZPs8h0A35AB9FLyapZspHOPuu+hdM7xwm9XaMxYIakrUkrQmjVreOqpp3jnnXdYv3593r8r54BLY8Sk+emREBIRD8JALWMFp65ISVhjAy6AiooKvvjFL3L00UeXVcCVBLWItUZ6JIQ0gVrGmkhdkVJkTQm4Kisr2Wuvvdhuu+2YNGkS++23H4ceeijdu3dvptyWJj2+QhpHj4SQZqJgrJHUFSnNqBAB1/Dhw+nYsWO979977z169epF166t89hW16TkpkdCSBGpm7IRsnZFHgcH/1FdkZKX5gy4Mtl5550bmk3JkwKxlkiPhJASoGAsTzm7In8euiLbFD9vUtKSCLik+BSIlTI9EkJKnIKxHNQV2eIsW7aM66+/nr59+1JVVUX//v2pqqqic+fOzbZMBVytmwKxYssUXKlrUVooBWMZqCuyRdp6663p0qULl156aZ3p2267bZ3ALPpvv3798rpzUAGXpKPB+s2pIXcnagC9tHAawB+oK7LF27hxI8OHD+fZZ5/N+zfdu3enZ8+e7LDDDmy33XZUVlbStm1bunXrF3b10AAAEoVJREFURvfu3amoqP9ImHQUcJUm3TXZEuQbdDWkRUykhWn1wZi6IstGdXU1e++9N0uXLm1SOu3bt+eggw7isMMOq/N6IAVcLYvumiwlzTVuS12LUgZadTeluiJbtJUrVzJ37lzmzJmz+d+NGzc2Or3KykoOOuggDj/8cPbff38FXJKRArFsNG5LpMFaXTCmrsgWJV3ANWfOHBYsWFCQ9Dt27MioUaO49tpr6d27d0HSlPKmQCxFj4QQKZhWE4ypK7JkNXfAFbfNNttw2mmn8dOf/pSePXs2yzKkPLW+QEyPhBApirIPxtQVWRKKHXDF9e7dm9GjR3PhhRc26yMupHyVRyCmR0KIlKSyDMbUFZmIYgRcZkb//v3Zc8892WOPPdhtt9248MIL2bBhQ715d9hhB37wgx/wrW99S2O/pElaXiDWkOBKXYsiiSurYExdkc0uiYBrzz33ZM8992T33XenU6dOm+f7xz/+US8I69u3L1deeSXnnntuXs8OE8mltAOxpo7bUiuXSEkoi2BMXZEFVUoBVyYTJ07c/P/+/fvzox/9iLPPPrvOYyhEmqo0niOWqWtRDzkVKSst8jlj6opskpUrV/L666/z6KOPsmDBAqqrq5k/fz4ff/xxwZbR1IArHecc/fr1o7KykquuuopRo0bRrl27guVZWpbye6Drrru6GXPm5H7avIIukbLTooIxdUXmrSW0cDXEokWLeOaZZzj99NNp27a0O4+k+ZVfINamjZsxcaJauURaqRYRjKkrMq1yC7hE8lF+T9bfeWeN2xJpxUp6zFjWrsgK2Of6VtEVqYBLpDiSCcS6d1fLl0grV5LBWM6uyAmw7SHFzVMzK1bAVVVVRefOnRk8eDBDhw5l0KBBCrhEKPW7JkWkrJVUMFbmXZFJt3C1bduWtm3b0qZNebckijSUAjERSVTiwViZdUUmHXCphUukYRSIiUjiEgvGWnBXZLEDrmjQpYBLpHAUiIlISSh6MNZCuiIVcImUNwViIlIyihKMlWhX5Guvvcb8+fOprq7mvffe2xx0KeASKW8KxESkpDRrMFYCXZFq4RKRKAViIlJymiUYK3JXpAIuEcmHAjERKUkFC8aauStSAZeINIUCMREpWU0OxgrYFVmsgKtnz54MGjSI/fffX4+FEGkFFIiJSElrdDDWyK7IpFq4Bg4cSKdOnRg4cCBmVrBliUhpUyAmIiWvQcFYnl2RK1fVMHfWy+pSFJFEFSQQM7OvALcCFcBdzrnrC5GuiEhKXsHYicszdkWucttw71tH89f7nmHOnF8r4BKRktDkQMzMKoDfAUcB1cB0M3vCOTe3qWmLiERlC8bmTXiMPTdcTmXF8nq/e2omfOO2pSxdNaHJyx8wYECd1/rsscceCrhEpNEK0SJ2APCuc24egJlNAE4CFIiJSMGlC8Y6d/6Er55yIW0r1taZd8NG+OEEuPlv4FzDlqGAS0SKoRCB2I5AtI2/GjiwAOmKiKRVU1PDmx0fYf3AXrR7Yx9qanoz9Z8/4sijf7x5ng8/gzN+C9PeyZyOAi4RSVohArF0t/fUu/Y0swuACwB22mmnAixWRMrdqlWreOihh/joo49w6Zq09qwGoN0b+/DS2oGsmG6M3N+FrkhYusrPpoBLREpVIQKxaqBv5HMf4OP4TM65O4A7AAYPHtyATgIRKXc5A65MDDYOmsX2g42vfecYjh/xRWYt+oj/1hzEBZfspYBLREpeIQKx6cCuZtYf+Ag4AzirAOmKSJlpdMAFtGnThp133pkTTzyRLl26pJ3nH8/OoG1bPZVHRFqOJtdYzrkNZnYJMBn/+Ip7nHNzmpwzEWmxmjvgykRBmIi0NAWptZxzfwX+Woi0RKTlSCrgEhEpF7p8FBGcc7z//vsMGDAg7fcKuEREmocCMZFWzDnH3Llzee655+jZsye9evVSwCUiUkQKxERaoZUrV3Lffffx2WefbZ62ePFi5s7N/RxmBVwiIoWjQEykjNXU1PDII4/w4YcfsmnTpgb9VgGXiEjzUyAmUgaaEnCltGnThvPPP5/tt9++wLkTEZFMFIiJtCBNCbgqKirYbbfdOO644+jcufPm6c45Vq5cyfLly1m/fn2hsywiIlkoEBMpQc0RcGViZnTr1o1u3bo1NrsiItJICsREElTMgEtEREqPAjGRIlDAJSIi6SgQE8nThg0bgOyv0VHAJSIiDaFATCSH9evX8+qrr/LKK69w4YUXAgq4RESkMBSIiWSwfv16pk2bxnPPPcfGjRsBuPbaa/P+vQIuERHJRYGYCLB69Wr+8pe/MG/evM1BV74UcImISGMpEJNWpSkBF0D//v055ZRTFHCJiEhBKBCTstSUgKtdu3YMHDiQI488ko0bN7Js2TKWL1/O8uXLadeuHZ06dWqmXIuISGujQExatEIEXCNGjMgaXG211VZNzaaIiEhaCsSkRShGwCUiIlJsCsSkpCjgEhGR1kSBmCRCAZeIiIgCMSmQ1atX89JLL7H77ruzww471JmugEtERCQ9BWLSJDU1Nbz44otMnz6dDRs28OKLLyrgEhERyZMCMWmQNWvW8NRTT/H2229vfvdiVLYgTAGXiIhIXQrEJK1UwPXOO++wfv36Bv1WAZeIiEh+FIi1ck0NuLbffnu23357ampqWLZsGZWVlZx55pm0bauiJSIikovOlq1EUwKuyspK9tprL4YPH07Hjh2bKYciIiKtjwKxMqOAS0REpOVQINZCKeASERFp+RSIlTgFXCIiIuVLgVgRLV26lJUrV9KvX7963yngEhERaX0UiBXBkiVLeP7553nttdc488wzefjhhxVwiYiIiAKx5lJbW8vEiRN5++232bRp0+bpDzzwQM7fKuASERFpHRSINVFtbS2TJ0/mzTffpLa2tkG/VcAlIiLSuikQy1NTAi4zo02bNmzcuJHtttuO8847Tw88FREREQVicY0NuMyMjh07svfeezNkyBA6dOiQNu3ly5ezdu1aBWIiIiLSegOx5gy4MunQoQPbbbddY7IrIiIiZajsA7EkAi4RERGRfJRNIKaAS0RERFqakgvEVqxYQbdu3TJ+r4BLREREykXJBGIffvghzz33HNtttx1HHnmkAi4REREpe4kHYu+88w5PPfUUK1asAOC9997jhRdeyPk7BVwiIiLS0iUSiH388ceMGzcur3kVcImIiEi5SrxFLK5z585cfPHFdOrUKemsiIiIiDSrRAKxiooKDj/8cA4++GDat2/PmjVrWLZsGcuXL2f58uUsXbpUgZiIiIiUvUQCsd69ezN06NDNnzt16kSnTp3Ycccdk8iOiIiISCLaJJ0BERERkdZKgZiIiIhIQhSIiYiIiCREgZiIiIhIQhSIiYiIiCREgZiIiIhIQhSIiYiIiCREgZiIiIhIQhSIiYiIiCREgZiIiMj/b+9+Xmyv6ziOv95o0CLDhYXQ1RTaJCoEgwQujPyBldi6KAQXbgoUEkvvnyBkCwO5tAkSIigRAskrtDUyU0M0kTDTkq60KGgR0qfFHUHq3rlz78y9r87M47Ga7zlfvucNH4Z5zud85wyUCDEAgBIhBgBQIsQAAEqEGABAiRADACgRYgAAJUIMAKBEiAEAlAgxAIASIQYAUCLEAABKhBgAQIkQAwAoEWIAACVCDACgRIgBAJQIMQCAEiEGAFAixAAASoQYAECJEAMAKBFiAAAlQgwAoESIAQCUCDEAgBIhBgBQIsQAAEqEGABAiRADACgRYgAAJUIMAKBEiAEAlAgxAIASIQYAUCLEAABKhBgAQIkQAwAoEWIAACVCDACgRIgBAJQIMQCAEiEGAFAixAAASoQYAECJEAMAKBFiAAAlewqxmXl4Zl6dmZdm5omZuXS/BgMAOOj2uiN2PMm1a63rk7yW5MG9jwQAcDjsKcTWWk+vtd7bPnw2yZG9jwQAcDjs5z1idyd5ah+vBwBwoF18phNm5pkkl5/iqaNrrSe3zzma5L0kj+9wnXuS3JMkV1555TkNCwBwkJwxxNZat+z0/MzcleSOJDevtdYO1zmW5FiSbG1tnfY8AIDD4owhtpOZuT3Jt5PctNb65/6MBABwOOz1HrFHk1yS5PjMvDAzj+3DTAAAh8KedsTWWp/ar0EAAA4bn6wPAFAixAAASoQYAECJEAMAKBFiAAAlQgwAoESIAQCUCDEAgBIhBgBQIsQAAEqEGABAiRADACgRYgAAJUIMAKBEiAEAlAgxAIASIQYAUCLEAABKhBgAQIkQAwAoEWIAACVCDACgRIgBAJQIMQCAEiEGAFAixAAASoQYAECJEAMAKBFiAAAlQgwAoESIAQCUCDEAgBIhBgBQIsQAAEqEGABAiRADACgRYgAAJUIMAKBEiAEAlAgxAIASIQYAUCLEAABKhBgAQIkQAwAoEWIAACVCDACgRIgBAJQIMQCAEiEGAFAixAAASoQYAECJEAMAKBFiAAAlQgwAoESIAQCUCDEAgBIhBgBQIsQAAEqEGABAiRADACgRYgAAJUIMAKBEiAEAlAgxAIASIQYAUCLEAABKhBgAQIkQAwAoEWIAACVCDACgRIgBAJQIMQCAEiEGAFAixAAASoQYAECJEAMAKBFiAAAlQgwAoESIAQCUCDEAgBIhBgBQIsQAAEqEGABAiRADACgRYgAAJUIMAKBEiAEAlAgxAIASIQYAUCLEAABKhBgAQIkQAwAoEWIAACVCDACgRIgBAJQIMQCAEiEGAFAixAAASoQYAECJEAMAKNmXEJuZ+2dmzcxl+3E9AIDDYM8hNjNXJLk1yZt7HwcA4PDYjx2xR5I8kGTtw7UAAA6NPYXYzNyZ5O211ou7OPeemXluZp47ceLEXl4WAOBAuPhMJ8zMM0kuP8VTR5M8lOS23bzQWutYkmNJsrW1ZfcMADj0zhhia61bTvX4zFyX5OokL85MkhxJ8vzM3LDWemdfpwQAOIDOGGKns9b6XZKPv388M28k2VprvbsPcwEAHHg+RwwAoOScd8T+21rrqv26FgDAYWBHDACgRIgBAJQIMQCAEiEGAFAixAAASoQYAECJEAMAKBFiAAAlQgwAoESIAQCUCDEAgBIhBgBQIsQAAEqEGABAiRADACgRYgAAJUIMAKBEiAEAlAgxAIASIQYAUCLEAABKhBgAQIkQAwAoEWIAACVCDACgRIgBAJQIMQCAEiEGAFAixAAASoQYAECJEAMAKBFiAAAlQgwAoESIAQCUCDEAgBIhBgBQIsQAAEqEGABAiRADACgRYgAAJUIMAKBEiAEAlAgxAIASIQYAUCLEAABKhBgAQIkQAwAoEWIAACVCDACgZNZaF/5FZ04k+eMFf+EL57Ik77aH4JxYu81m/Tab9dtcB33tPrnW+tj5uHAlxA66mXlurbXVnoOzZ+02m/XbbNZvc1m7c+etSQCAEiEGAFAixM6PY+0BOGfWbrNZv81m/TaXtTtH7hEDACixIwYAUCLEzrOZuX9m1sxc1p6F3ZmZh2fm1Zl5aWaemJlL2zOxs5m5fWZ+PzOvz8x32vOwezNzxcz8cmZemZmXZ+be9kycnZm5aGZ+OzM/b8+yiYTYeTQzVyS5Ncmb7Vk4K8eTXLvWuj7Ja0keLM/DDmbmoiTfT/KFJNck+crMXNOdirPwXpJvrbU+neSzSb5h/TbOvUleaQ+xqYTY+fVIkgeSuBFvg6y1nl5rvbd9+GySI815OKMbkry+1vrDWutfSX6c5MvlmdiltdZf1lrPb3/9j5z8gf6J7lTs1swcSfKlJD9oz7KphNh5MjN3Jnl7rfViexb25O4kT7WHYEefSPKnDxy/FT/IN9LMXJXkM0l+1Z2Es/C9nNxw+Hd7kE11cXuATTYzzyS5/BRPHU3yUJLbLuxE7NZOa7fWenL7nKM5+bbJ4xdyNs7anOIxu9AbZmY+kuSnSe5ba/29PQ9nNjN3JPnrWus3M/O59jybSojtwVrrllM9PjPXJbk6yYszk5x8a+v5mblhrfXOBRyR0zjd2r1vZu5KckeSm5fPePl/91aSKz5wfCTJn0uzcA5m5kM5GWGPr7V+1p6HXbsxyZ0z88UkH07y0Zn50Vrra+W5NorPEbsAZuaNJFtrrYP8D1EPjJm5Pcl3k9y01jrRnoedzczFOflHFTcneTvJr5N8da31cnUwdmVO/rb6wyR/W2vd156Hc7O9I3b/WuuO9iybxj1i8L8eTXJJkuMz88LMPNYeiNPb/sOKbyb5RU7e6P0TEbZRbkzy9SSf3/5+e2F7hwUOBTtiAAAldsQAAEqEGABAiRADACgRYgAAJUIMAKBEiAEAlAgxAIASIQYAUPIf8whyhtRYrkcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Figure setup.\n",
    "scale = 10\n",
    "origin = np.array([0,0])\n",
    "plt.axis([-scale/2,scale/2,-scale/2,scale/2])\n",
    "plt.title(\"An affine subspace L. A scaling of the black vector by some value lambda will \\n move the orange vector parallel to the black, 'supported' by the purple.\", size=15)\n",
    "# Figure setup.\n",
    "\n",
    "# Data setup.\n",
    "lam = 1\n",
    "x0 = np.array([-1,1])\n",
    "x1 = np.array([3,.5])\n",
    "val = x0+lam*x1\n",
    "x1s = np.vstack([l*x1 for l in np.linspace(-4,4,25)]) # Grey lines\n",
    "# Data setup.\n",
    "\n",
    "# Plotting vectors.\n",
    "plt.quiver(*origin, x1s[:,0],x1s[:,1], width=.003, scale=scale, color=\"grey\")\n",
    "plt.quiver(*origin, *x1, scale=scale, color=\"k\")\n",
    "plt.quiver(*origin, *x0, scale=scale, color=\"blueviolet\")\n",
    "plt.quiver(*origin, *val, scale=scale, color=\"orange\") #L = x_0 + lambda * x_1 ; Affine subspace\n",
    "# Plotting vectors.\n",
    "\n",
    "# Plotting subspace.\n",
    "# Arbitrary choice of 250 points on the subspace. Subspace is any infinite amount of points along the line.\n",
    "val = np.vstack([x0+l*x1 for l in np.linspace(-4,4,250)]) \n",
    "plt.scatter(val[:,0],val[:,1],color=\"r\", s = .5)\n",
    "# Plotting subspace.\n",
    "\n",
    "plt.legend([\"$x_1*\\lambda$\",r\"$x_1$\",r\"$x_0$\",\"y\",r\"$L = x_0 + \\lambda x_1$\"]);"
   ]
  }
 ],
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  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
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  "language_info": {
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