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MathGroup Archive 2003

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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


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