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From: "Pinpress" <nothing@nothing.edu>
Newsgroups: comp.soft-sys.matlab
Subject: Re: Solving AM = MB
Date: Sat, 22 Nov 2008 21:28:02 +0000 (UTC)
Organization: Dartmouth College
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Sorry John, I did not quite understand.

All my matrices, X, Ai, Bi, are 4-by-4 square matrix. My gut feeling is that, although for each X*A = B*X equation, there many possible X's to satisfy, but there should be a unique one that satisfies all the equations because all the equations are derived from physical quantities.  Then I am kind stuck on how to find it.

"John D'Errico" <woodchips@rochester.rr.com> wrote in message <gg9sua$4gv$1@fred.mathworks.com>...
> "Pinpress" <nothing@nothing.edu> wrote in message <gg9qui$9si$1@fred.mathworks.com>...
> > I see -- sorry I overlooked.
> > 
> > So here is my real problem to solve:
> > 
> > I have many equations like:
> > 
> > X*A1 = B1*X;
> > X*A2 = B2*X;
> >  etc.
> > 
> > And I know X is orthogonal, because it is a rigid transformation matrix. How do I construct or recover a sensible X from these equations? Thanks for any input.
> > 
> 
> You can stack many of these on top of each other, solving
> for one overall matrix. 
> 
> But you cannot build in the requirement of orthogonality into
> a linear least squares solution.
> 
> John