Definition of the matrix-vector operator of division of Julia

Question

I stumbled upon something that I find very strange.

As an example, consider the code

A = reshape(1:6, 3,2)
A/[1 1]

which gives

3×1 Array{Float64,2}:
 2.5
 3.5
 4.5

As I understand it, in general, such a division gives the weighted average value of the columns, where each weight is inversely proportional to the corresponding element of the vector.

So my question is: why is it defined this way?

What is the mathematical rationale for this definition?

Answer 1

|A - v*[1 1]|₂ - , , (.. v , ). / \ , , . , , , Matlab Octave, , .

Answer 2

A - NxN, b - - Nx1. \ Ax=b, / xA=b.

, . QR SVD. . , , . : OLS , .

, ? . , . , . , - O (n ^ 3), . , , . , \ ( /, \), (LU, QR, SVD, Cholesky ..) , - MATLAB. , , . IterativeSolvers.jl, Ax=b.

, Ax=b , . , , , Ax=b . \ () .