In the following example, it seems that the Matrix division `\`

does not provide an intended computation.

Let `x= A'\b`

, then if `norm(A'*x-b, Inf)`

is zero such that `A'x-b == 0`

, then `b`

is a linear combination of rows from `A`

(`b`

lies in the row space of `A`

).

I am using Matrix division `\`

to test if `b`

lies in the row space of `A`

or not, and find that the `\`

gives a result different from the result by the *reduced row echelon form*. Hence, I compute it by hand, the `norm(A'*x-b, Inf)`

is 4.755666482359269e-12, but the result from Matrix division is 0.00010237, far from zero (tolerance)

Download matH.jls first.

```
using LinearAlgebra, Serialization
function loadData(fn)
#load data
local t
open(fn, "r") do io
t = deserialize(io)
end
return t
end
function main()
H, v = loadData("./matH.jls")
G = qr(H', ColumnNorm())
z = G.P*inv(G.R)*Matrix(G.Q)'*v
display(norm(H'*z-v, Inf)) #4.755666482359269e-12
z1 = G\v
display(norm(H'*z1-v, Inf)) #0.00010237343843657264
end
main()
nothing
```

From the \(A,B) , the docstring of Julia: " For rectangular `A`

the result is the minimum-norm least squares solution computed by a pivoted QR factorization of `A`

and a rank estimate of `A`

based on the R factor."

Is there any setting I can choose when using Matrix division `\`

in Julia?

Edit: more discussions on `x=A\b` by `qr(A, ColumnNorm()) \ B`, Matrix division does not yield `Ax=b` · Issue #49625 · JuliaLang/julia · GitHub