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

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*To*: eigen@xxxxxxxxxxxxxxxxxxx*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*Dkim-signature*: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:mime-version:received:in-reply-to:references :date:message-id:subject:from:to:content-type :content-transfer-encoding; bh=PmOtKRu8Nm7LvxRYpvnXPSo0rduqPchJ51XsriTfG68=; b=bs2gFJROPF2/6uUgN4IepcrKpk8Q4taSanzgCec5Az0E23+poHK71tTNrepSqKSno2 EZimo15Y3dp/FQiwV3fKapK1bEs4ZenYruUN5DE09vo5V3UDiStLdgbx1mcuxHWZcpvY GWZwYFe/py6oWdxFlDvnAo3dGP/hYu+JpMKu0=*Domainkey-signature*: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=mime-version:in-reply-to:references:date:message-id:subject:from:to :content-type:content-transfer-encoding; b=DjMiGOJJlV7c76xeXTxl0RLasB4ubNAHB3OtuOoURI3anbFeIp2bD3bly5l6QW8Pf6 fj9moktfvScDQ5xVGnaO8QPpmvLWxW72Y0U8d/BDWkStVMBHViHBLVpHq3v+8++O4Mum cKyZ5pIJWoW+LJ8ahpmsKzKUgoAqh6tQaY8Bw=

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. Keir On Fri, Jan 30, 2009 at 8:34 AM, W. James MacLean <james.maclean@xxxxxxxxxxx> wrote: > Hi, > > 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 > matrix? > > 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. > > Cheers, > > James > > PS- I *really really* like what I've seen of Eigen so far - way cool! > > > > >

**Follow-Ups**:**Re: [eigen] Computing left nullspace of A when rows > cols***From:*Benoit Jacob

**References**:**[eigen] Computing left nullspace of A when rows > cols***From:*W . James MacLean

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