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Find orthogonal complement for given matrix

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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

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Accepted Answer

Vladimir Sovkov
Vladimir Sovkov on 30 Jan 2020
B=null(A');
The matrix transposing is important!

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