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