### Orthonormal basis of a Null Space

Posted:

**Sat Oct 27, 2012 6:22 am**Hi There,

I am trying to find the orthonormal basis of the null space as defined by the matrix A (mxn).

I tried the following steps:

1) Did the QR decomposition on the transpose of A using DGEQRF.

2) Directed the resulting output of A to DORMQR.

I was expecting the last (n-m) columns of C should contain the orthonormal basis of the null space but does not seem so.

Could you pls clarify if these are the right steps?

I have also tried DGESVD and it worked correctly as long as m is 1. When m happened to be greater than 1 but less than n, this method didn't give correct results.

Are there any other methods?

Regards,

Vivek.

I am trying to find the orthonormal basis of the null space as defined by the matrix A (mxn).

I tried the following steps:

1) Did the QR decomposition on the transpose of A using DGEQRF.

2) Directed the resulting output of A to DORMQR.

I was expecting the last (n-m) columns of C should contain the orthonormal basis of the null space but does not seem so.

Could you pls clarify if these are the right steps?

I have also tried DGESVD and it worked correctly as long as m is 1. When m happened to be greater than 1 but less than n, this method didn't give correct results.

Are there any other methods?

Regards,

Vivek.