|Re: [eigen] Computing left nullspace of A when rows > cols|
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- Subject: Re: [eigen] Computing left nullspace of A when rows > cols
- From: Keir Mierle <mierle@xxxxxxxxx>
- Date: Fri, 30 Jan 2009 09:20:56 -0800
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Just to second a request for this: Many applications use the SVD to
form a basis for the nullspace of A, where A is 'wide'; this is the
same here as the left nullspace of a 'tall' matrix.
In libmv, I solve this problem by padding wide matrices with zeros on
the bottom until they are square, then pass to the SVD. Suboptimal,
but it works well enough for now.
I will see about the SVD later this week.
On Fri, Jan 30, 2009 at 8:34 AM, W. James MacLean
> I would like to use Eigen to compute the left nullspace of a matrix A where
> A is n by m, and n > m. Assuming we denote the decomposition as A = U S
> V^*, then (currently) the U returned by Eigen is n by m, and the columns
> corresponding to the left nullspace are missing.
> Is it possible to either (1) compute these easily using some other facility
> already in Eigen, or (2) modify Eigen so it outputs the full n by n U
> I know that, generally, I could do this by transposing A and computing the
> right nullspace, but then cols > rows and Eigen doesn't seem to support
> this for SVD at present.
> PS- I *really really* like what I've seen of Eigen so far - way cool!