mrdivide undocumented feature?

I have A = [0 1 ; 3 2] and B = [1 2]. For A / B, I get [0.4 ; 1.4], which is a least squares solution. Here is my problem: where is this documented? I can't see this case covered in the documentation of the mrdivide function. The documentation does say that a least-squared solution is obtained when A is rectangular, but when A is square, all it says is: " If A is a square n-by-n matrix and B is a matrix with n columns, then x = B/A is a solution to the equation x*A = B, if it exists." Since no solution exists, shouldn't it return an error? Or at least, shouldn't the behaviour be documented?

Answer 1

[Titus Edelhofer]

Hi,

I think you might have mixed up A and B from the doc with A and x from your computation:

A/x

In this case your A corresponds to the B where x corresponds to A from doc. And yes, in this case A from doc (your x) is rectangular and B (your A) has n(=2) columns. Everything fine ...

Titus

[PeterB]

But the documentation specifically says, " If A is a rectangular m-by-n matrix with m ~= n". i.e. m and n must not be equal. The documentation makes no provision for a least squares answer if A is square, as far as I can see.

You're right about the mixing of x and B in my question, though. So that my question matches the documentation, I've gone back and replaced x with B in my question, but I think my problem still stands.

[Titus Edelhofer]

Hi Peter,

sorry, but it's still the other way round:

A = [1 2];
B = [0 1 ; 3 2];
x = B / A

now we have indeed: A is m by n with m~=n and B has n columns. Note, the doc talks about B / A, you wrote A / B.

Titus

[PeterB]

Duh! OK, now I've got it. Thanks!

[Titus Edelhofer]

Your welcome, glad I could help. You may mark the question then as answered, if you like ...