Re: How to compute a MatrixPower using: A^n = P D^n Inverse[P]

• To: mathgroup at smc.vnet.net
• Subject: [mg34991] Re: [mg34976] How to compute a MatrixPower using: A^n = P D^n Inverse[P]
• From: Daniel Lichtblau <danl at wolfram.com>
• Date: Tue, 18 Jun 2002 02:48:32 -0400 (EDT)
• References: <200206170726.DAA18874@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```"J. Guillermo Sanchez" wrote:
>
> I have the matrix
>
> A == {{3,1,0},{1,2,-1},{0,-1,3}}
>
> For educational purpose I would like to evaluate
>
> A^n (* I mean MatrixPower[A,n]*)
>
> using the following matrix property
>
> A^n == P D^n Inverse[P]  (*D mean Diagonal Matrix *)
>
> How can I do with Mathematica? (Methods to obtain P and D)
>
> Thanks
>
> Guillermo Sanchez

This is in the help browser under Eigensystem.

http://documents.wolfram.com/v4/RefGuide/Eigensystem_ex.html

Daniel Lichtblau
Wolfram Research

```

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