machine learning/matrix_operations.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "matrix operations.ipynb",
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "# Matrix operations for machine learning\n",
        "\n",
        "![matrixes](https://images.unsplash.com/photo-1573512443418-c6768862dda7?ixlib=rb-1.2.1&ixid=MnwxMjA3fDB8MHxwaG90by1wYWdlfHx8fGVufDB8fHx8&auto=format&fit=crop&w=1074&q=80)\n",
        "\n",
        "\n",
        "photo by [Derek Mckinney](https://unsplash.com/@derickray) at [Unsplash](https://unsplash.com/)\n",
        "\n",
        "\n",
        "## Introduction\n",
        "\n",
        "this is the companion colab code for my tutorial in medium about matrix operation introduction in Python , please read the article for better understanding of the code.  \n",
        "this is a colab notebook, you can test in colab (all the code has been tested and you do not need to set your machine)\n",
        "\n",
        "[article](https://)\n",
        "\n",
        "\n",
        "\n",
        "note: the articles will be publish soon"
      ],
      "metadata": {
        "id": "FesykKbv6Bo7"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "id": "333RfsWsucEk"
      },
      "outputs": [],
      "source": [
        "import numpy as np"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#matrix\n",
        "A = np.array([[1,2],[3,4]])\n",
        "B = np.array([[5,6],[7,8]])\n",
        "print(A)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "2zy7EfHJuiCJ",
        "outputId": "3d7d72dd-811a-4659-fe70-44362804d5f6"
      },
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[1 2]\n",
            " [3 4]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#slice of matrix\n",
        "#a row\n",
        "print(A[1,:])\n",
        "#a column\n",
        "print(A[:,1])"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "WGN6uzW5vZrE",
        "outputId": "5bc947ea-823f-4d1c-d07d-efe68119a9fa"
      },
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[3 4]\n",
            "[2 4]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#addition\n",
        "C= A + B\n",
        "C"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "pMYFeUTrvt0l",
        "outputId": "f5ae42f7-5384-4512-a9d6-aa4bf520403e"
      },
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 6,  8],\n",
              "       [10, 12]])"
            ]
          },
          "metadata": {},
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#subtraction\n",
        "C= A - B\n",
        "C"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "9sK4Tck7vzSf",
        "outputId": "aad4e365-acf3-4e37-da5e-d839e0da27a3"
      },
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[-4, -4],\n",
              "       [-4, -4]])"
            ]
          },
          "metadata": {},
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#hadamard product, element-wise\n",
        "C= A * B\n",
        "C"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "l-YdiVo2v5do",
        "outputId": "066d311c-a765-4e12-8a99-b42112e1bf50"
      },
      "execution_count": 40,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 5., 12.],\n",
              "       [21., 32.]])"
            ]
          },
          "metadata": {},
          "execution_count": 40
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#dot product\n",
        "#you can also use np.dot()\n",
        "C= A @ B\n",
        "C"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "wL1a49KmwIlM",
        "outputId": "87af148b-324e-4d43-bf6f-612a94d45f18"
      },
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[19, 22],\n",
              "       [43, 50]])"
            ]
          },
          "metadata": {},
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#transpose of a matrix\n",
        "A_T = A.T\n",
        "A_T"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Ma65bIapwX4L",
        "outputId": "1a86f462-6432-4af3-b93b-952850d8ce77"
      },
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1, 3],\n",
              "       [2, 4]])"
            ]
          },
          "metadata": {},
          "execution_count": 15
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#identity matrix \n",
        "I = np.eye(2)\n",
        "I"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "qGzv8XhVwNNT",
        "outputId": "a0938efa-2e84-4a30-9ee3-d97d14f75bda"
      },
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1., 0.],\n",
              "       [0., 1.]])"
            ]
          },
          "metadata": {},
          "execution_count": 13
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#inverse of a matrix\n",
        "inv_A = np.linalg.inv(A)\n",
        "inv_A"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "TM9D72SnwjdU",
        "outputId": "b2478597-306b-4866-8fb0-f7fd9be6ada5"
      },
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[-2. ,  1. ],\n",
              "       [ 1.5, -0.5]])"
            ]
          },
          "metadata": {},
          "execution_count": 18
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#A * inv_A = I\n",
        "#let's check if it is equal to the identity matrix\n",
        "np.allclose(np.dot(inv_A, A), np.eye(2))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "WIEnLJAjw6H6",
        "outputId": "5fc49a8c-3a41-468e-e312-0bcb9532d74c"
      },
      "execution_count": 30,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "True"
            ]
          },
          "metadata": {},
          "execution_count": 30
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#matrix division\n",
        "A.dot(np.linalg.inv(B))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "tyy76-fQymVB",
        "outputId": "33db8df3-88d3-41d2-ee82-3dc19d3676f6"
      },
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 3., -2.],\n",
              "       [ 2., -1.]])"
            ]
          },
          "metadata": {},
          "execution_count": 34
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#linear equation for x\n",
        "b= [0.5, 2]\n",
        "x = np.linalg.inv(A).dot(b)\n",
        "x"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "tfX8qXn-yuW_",
        "outputId": "7d7d3956-7fb3-4085-b142-1d3605eb784b"
      },
      "execution_count": 36,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 1.  , -0.25])"
            ]
          },
          "metadata": {},
          "execution_count": 36
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#linear equation for X\n",
        "X = B.dot(np.linalg.inv(A))\n",
        "X"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "G9p-SnDQzX49",
        "outputId": "1030398c-83c3-4352-f034-aa57b3845394"
      },
      "execution_count": 38,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[-1.,  2.],\n",
              "       [-2.,  3.]])"
            ]
          },
          "metadata": {},
          "execution_count": 38
        }
      ]
    }
  ]
}