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## [Help-gsl] Compute null space of a matrix using SVD

**From**: |
Christophe Dehais |

**Subject**: |
[Help-gsl] Compute null space of a matrix using SVD |

**Date**: |
Sat, 21 Mar 2009 18:10:07 +0100 |

I'm trying to compute the null space of a matrix A with M < N, using
the residual singular vectors of the SVD decomposition of A.
However, as the SVD code doesn't allow M < N, I have to work on A tanspose.
I could use the fact that if A' = U.S.V' then A = V.S.U' and return
the last vectors of U, but U is actually truncated because we compute
a thin SVD,
so some (or all in case M is full rank) vectors of M's null space are lost.
I'm guessing that either the SVD code should support the case M < N or
there should be an option to compute the full SVD decomposition.
Or is there another alternative I could use ?
thanks,
Christophe

**[Help-gsl] Compute null space of a matrix using SVD**,
*Christophe Dehais* **<=**