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From: "Per Sundqvist" <per.sundqvist@live.com>
Newsgroups: comp.soft-sys.matlab
Subject: Re: How to solve TA = BT
Date: Wed, 14 Jan 2009 16:22:02 +0000 (UTC)
Organization: Chalmers Tekniska H&#246;gskola
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"Pinpress" <nospam__@yahoo.com> wrote in message <gkkqeh$idk$1@fred.mathworks.com>...
> Hi all,
> 
> I wonder if there is an existing program that solves the matrix equation: TA = BT, in which T is to be solved, all matrices (T, A, B) are 4-by-4 matrices.  In addition, it is prior information that all matrices are rigid-body transformation matrices, so T only has 12 unknowns. 
> 
> Please also note that I have many equations similar to the one given, so:
> 
> T*A1 = B1*T;
> T*A2 = B2*T; 
> ...
> T*An = Bn*T;
> 
> In all of the equations, T should be the same. So my question is, how to solve T? thanks for any input. 

T=0 is an obvious solution. If you write a vector t=[t11 t12 t13 ...t44]', then you could show that your equation for T is:

C*t=0

where Cij=f(A,B) a linear combination of elements in A and B. Could there be another solution than t=[0 0 0 ...0]? Perhaps under special conditions on A and B?

/Per