Find orthogonal complement for given matrix

Hi everyone,

I am not sure if the term "orthogonal complement" is well adapted for my case but here is what I would like to do:

I have a matrix A, not necessary square, and I want to find a matrix B such that:

B^T * A = 0

B^T * B = I (identity)

Here is an example :

A = [1 0; 0 1; 0 0];

The null command returns the null space of the matrix, which is empty.

But here a solution is

B = [0; 0; 1];

I have indeed :

B' * A = [0 0];
B' * B = 1;

Is there a way to find this matrix B for more complex examples ?

Best wishes,

Peter

Answer 1

[Vladimir Sovkov]

B=null(A');

The matrix transposing is important!