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From: "Tim Davis" <davis@cise.ufl.edu>
Newsgroups: comp.soft-sys.matlab
Subject: Re: How to solve XA + B = 0?
Date: Fri, 3 Jul 2009 16:55:03 +0000 (UTC)
Organization: University of Florida
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..
> > "Tao Shen" <tshen@mathworks.com> wrote in message 
> > > I need to solve a equation which is XA + B =0. It is a least squares 
> > > problem.
> > > 
> > > The X is a 2*N matrix, A is N*2, and B is 2*2. Because A is N*2, it seems we 
> > > can't find its right inverse matrix but only left inverse matrix. However it 
> > > is not useful in this case.

Don't let that INV go past your eyes; to solve that system FACTORIZE
(see my file on the file exchange by that name).

> I have no idea (yet) how to find the X with minimum (global) 2-norm.

You can use QR to get a min 2 norm solution of an underdetermined
system, by factorizing A'.  That's what I do in the FACTORIZE package.
x=A\b or b/A gives a basic solution to an underdetermined system,
not a min 2norm solution.