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Re: Eigensystems

• To: mathgroup at smc.vnet.net
• Subject: [mg18924] Re: Eigensystems
• From: adam.smith at hillsdale.edu
• Date: Tue, 27 Jul 1999 22:17:26 -0400
• Organization: Deja.com - Share what you know. Learn what you don't.
• References: <7nef9i$238@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Perhaps I do not fully understand the question.  But assuming that
lambda is a scalar constant and both A and B are square n-by-n
matrices.  Then the following solves for the eigensystem

Eigensystem[ Inverse[B].A ]

returning the eigenvalues and associated eigenvectors.  Any
misunderstanding may lie in what you mean by "efficient".  Some quick
tests show that as long as A and B are assigned numeric values and not
simple symbolic letters, Mathematica returns a solution very rapidly.
However, if you what a complete symbolic answer things get very messy
and can take a considerable amount of time and require a great deal of
memory.  I solved a 2-by-2 system rather quickly, but the output answer
was very long.

Adam Smith

In article <7nef9i$238 at smc.vnet.net>,
  Tony Harker <ahh at baker.phys.ucl.ac.uk> wrote:
>
>   Can anybody recommend an efficient method for solving the modified
> eigensystem
>        A x = lambda B x
> numerically in Mathematica?
>
>    Tony Harker
>
> __________________________________________________________________
> |  Dr A.H. Harker                                                |
> |  Director of Postgraduate Studies                              |
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