       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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