Documentation update for LinearAlgebra functions

stdlib/LinearAlgebra/src/LinearAlgebra.jl

@@ -197,7 +197,8 @@ abstract type PivotingStrategy end
     NoPivot
 
 Pivoting is not performed. Matrix factorizations such as the LU factorization
-may fail without pivoting.
+may fail without pivoting, and may also be numerically unstable for floating-point matrices in the face of roundoff error.
+This pivot strategy is mainly useful for pedagogical purposes.
 """
 struct NoPivot <: PivotingStrategy end
 
@@ -206,6 +207,11 @@ struct NoPivot <: PivotingStrategy end
 
 First non-zero element in the remaining rows is chosen as the pivot element.
 
+Beware that for floating-point matrices, the resulting LU algorithm is numerically unstable — this strategy
+is mainly useful for comparison to hand calculations (which typically use this strategy) or for other
+algebraic types (e.g. rational numbers) not susceptible to roundoff errors.   Otherwise, the default
+`RowMaximum` pivoting strategy should be generally preferred in Gaussian elimination.
+
 Note that the [element type](@ref eltype) of the matrix must admit an [`iszero`](@ref)
 method.
 """
@@ -214,7 +220,9 @@ struct RowNonZero <: PivotingStrategy end
 """
     RowMaximum
 
-The maximum element in the remaining rows is chosen as the pivot element.
+The maximum-magnitude element in the remaining rows is chosen as the pivot element.
+This is the default strategy for LU factorization of floating-point matrices, and is sometimes
+referred to as the "partial pivoting" algorithm.
 
 Note that the [element type](@ref eltype) of the matrix must admit an [`abs`](@ref) method,
 whose result type must admit a [`<`](@ref) method.
@@ -224,7 +232,8 @@ struct RowMaximum <: PivotingStrategy end
 """
     ColumnNorm
 
-The column with the maximum norm is used for subsequent computation.
+The column with the maximum norm is used for subsequent computation.  This
+is used for pivoted QR factorization.
 
 Note that the [element type](@ref eltype) of the matrix must admit [`norm`](@ref) and
 [`abs`](@ref) methods, whose respective result types must admit a [`<`](@ref) method.

stdlib/LinearAlgebra/src/matmul.jl

@@ -694,7 +694,7 @@ parameter `tM` as follows:
 | --- | :--- | :--- |
 | `'N'` | `B[ir_dest, jr_dest]` | `M[ir_src, jr_src]` |
 | `'T'` | `B[ir_dest, jr_dest]` | `transpose(M)[ir_src, jr_src]` |
-| `'C'` | `B[ir_dest, jr_dest]` | `adjoint(M)[ir_src, jr_src]` |
+| `'C'` | `B[ir_dest, jr_dest]` | `conj(transpose((M))[ir_src, jr_src]` |
 
 The elements `B[ir_dest, jr_dest]` are overwritten. Furthermore, the index range
 parameters must satisfy `length(ir_dest) == length(ir_src)` and