Re: solving for multiple matrices

> -----Original Message-----
> From: Andras Balogh [mailto:[email protected]]
> Sent: Thursday, September 17, 2009 12:38 PM
> To: [email protected]
> Subject: [Algorithms] solving for multiple matrices
>
> Hi, I have a chain of transformations with multiple unknown (but fixed!) transforms. What I do know is the end result transformation and some of the transformations in between, and I know these for multiple frames. So
>  from here, I'd like to compute the unknowns. Here it is in more formal
> version:
>
> I'd like to find 2 unknown matrices X and Y. I have 4 known matrices A1, A2, B1 and B2, and also know this:
> A1 = X * B1 * Y
> A2 = X * B2 * Y
>
> I can compute X from the first equation:
> X = A1 * Y^-1 * B1^-1
>
> And substitute it into the second:
> A2 = A1 * Y^-1 * B1^-1 * B2 * y
>
> Assigning:
> C = A1^-1 * A2
> D = B1^-1 * B2
>
> Then it becomes:
> C = Y^-1 * D * Y
>
> Now, how do I solve this for Y? This form lookes strangely familiar, but I cannot figure out what to do from here (wish I knew how to Google this ;).
> Hopefully there's an analytic solution to this. Any ideas?
>
> Thanks,
>
>
>
> Andras

It has the form of a similarity transformation, if that helps.
http://mathworld.wolfram.com/SimilarityTransformation.html

Similarity transforms preserve eigenvalues and consequently the trace
and determinant of the matrix applied to, so if C and D don't have the
same trace and determinant, then your Y doesn't exist.

--bb

------------------------------------------------------------------------------
Come build with us! The BlackBerry® Developer Conference in SF, CA
is the only developer event you need to attend this year. Jumpstart your
developing skills, take BlackBerry mobile applications to market and stay 
ahead of the curve. Join us from November 9-12, 2009. Register now!
http://p.sf.net/sfu/devconf
_______________________________________________
GDAlgorithms-list mailing list
[email protected]
https://lists.sourceforge.net/lists/listinfo/gdalgorithms-list
Archives:
http://sourceforge.net/mailarchive/forum.php?forum_name=gdalgorithms-list