Solving a matrix equation

*To*: mathgroup at smc.vnet.net*Subject*: [mg44266] Solving a matrix equation*From*: josegomez at gmx.net*Date*: Tue, 4 Nov 2003 03:23:36 -0500 (EST)*Organization*: Sheffield University*Sender*: owner-wri-mathgroup at wolfram.com

Hi, As a test of my calculations, I would like to solve a matrix equation using Mathematica. It is a symbolic problem, but I can't get my head round it. Let T and Q be two nxn complex matrices (T is Hermitian, Q is not). I want to test whether a vector p (nx1) is an eigenvector of the following combination: A=(Inverse[T]*Q)*(Inverse[T]*Conjugate[Transpose[Q]]), or, in LaTeX form: (T^{-1}Q)*(T^{-1}*Q^{*T}. I have punched the previous lines into Mathematica, and tried to see whether my vector p was an eigenvector. However, I had Mathematica eat up all the memory and subsequently crash, so I am asking here to see whether someone can suggest a way around this. The problem is 3x3 (n=3), but due to the relatively large number of parameters, it is complicated and error-prone to do by hand. (and if it hasn't showed up yet, I am very much a newbie at Mathematica!) Many thanks for your time, Jose

**Follow-Ups**:**Re: Solving a matrix equation***From:*Daniel Lichtblau <danl@wolfram.com>