zgsevd for Ax=0

[Zahra]

Dear all,

I want to find the nontrivial solutions of the complex general matrix. Can I use zgsevd routine? Is it always helpful?

Bests,
Zahra

[Julien Langou]

Yes you may use ZGESVD to compute an orthogonal basis for the Nullspace of a complex general matrix.
Julien.

[Zahra]

thank you very much for your reply. I found somewhere that
The columns of V corresponding to zero elements of D span the null-space
I have 16by16 matrix. Would you please let me know that the parameter which shows the x is a column of U or V?

Bests.

[Julien Langou]

X is the 16th column of the VT matrix in your case.
(Please check that S(16) is indeed small, and that AX = 0.)

[Zahra]

Dear Julien,

I used the routine for finding the X of AX=0. But while S(16) is small (in order of 10^-8), AX is of order of 10^-1. Here, I've taken the 16 column of VT to be X. Indeed this X can't be the solution of AX=0. Am I doing something wrong? would you please help?

Also, is there any other method that I can use to find the nontrivial solutions of AX=0?

Bests