Re: [eigen] Computing left nullspace of A when rows > cols

[Benoit Jacob <jacob.benoit.1@xxxxxxxxx>]

2009/1/30 W. James MacLean <james.maclean@xxxxxxxxxxx>:
> Thanks Benoit!
>
> left_nullspace(A) = span({x | x^T A = 0}), where A is n by m, and x is an n
> by 1 vector.
>
> If you compute an SVD of A in Matlab, for example, the U is an n by n
> orthogonal matrix, and V is an m by m orthogonal matrix. The last n-m
> columns of U provide a basis for the left nullspace.
>
> In the case where n > m, the contents of the last n-m columns of U multiply
> into the 0 rows of the (nominally) n by m S matrix, and thus disappear. So
> while you don't need the last n-m columns of U to make the product U S V^*
> work, not having them means you don't get a basis for the left nullspace of
> A.
>
> Does that describe it well enough?

Yes, thanks!
Benoit