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MathGroup Archive 2002

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Re: information on Eigensystem

  • To: mathgroup at smc.vnet.net
  • Subject: [mg33610] Re: information on Eigensystem
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Wed, 3 Apr 2002 18:08:14 -0500 (EST)
  • Organization: Universitaet Leipzig
  • References: <a890u0$nto$1@smc.vnet.net> <a8br2m$3lg$1@smc.vnet.net> <a8e6sd$7k9$1@smc.vnet.net>
  • Reply-to: kuska at informatik.uni-leipzig.de
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

the problem is, you have typed "i" instead of I or \[ImaginaryI].
Mathematica has to find the analytical eigen system of a 4 x 4
matrix with a *variable*, i.e., solve a equation of degree 4, insert 
the huge expression for the eigenvalues and compute the eigenvectors. 
This can take several hours. If you type

M = {{65, 3 + 6\[ImaginaryI], 12 - 6\[ImaginaryI], 
      4 - 2\[ImaginaryI]}, {3 - 6\[ImaginaryI], 30, 0, 
      30}, {12 + 6\[ImaginaryI], 0, 9, 3}, {4 + 2\[ImaginaryI], 30, 3,
46}}

the exakt solution needs only a few seconds.

Regards
  Jens

Bettina wrote:
> 
> Hi
> I have another question concerning Eigensystem: I try to get the
> Eigensystem for heritian (complex) matrices. Following my test matrix
> M={{65,3+6i,12-6i,4-2i},{3-6i,30,0,30},{12+6i,0,9,3},{4+2i,30,3,46}}.
> But if I try to get Eigensystem[M] nothing comes up. What could be the
> problem? I have already found out (archive) that there seem to be some
> special effects when using Eigensystem on complex matrices, but these
> messages dated from 1999 and 2000. Has anything changed since then? Is
> there a way to solve my problem?
> Thanks for help
> Bettina


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