- 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.
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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 | > | Department of Physics and Astronomy /\ | | | | | > | (Centre for Materials Research) /--\ |---| |---| | > | University College / \o| |o| |o | > | Gower Street ---------------------- | > | LONDON | > | WC1E 6BT | > | Tel (44) (0)207 679 3404 | > | Fax (44) (0)207 679 7145 | > | E-mail A.Harker at ucl.ac.uk | > |________________________________________________________________| > > Sent via Deja.com http://www.deja.com/ Share what you know. Learn what you don't.