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

• To: mathgroup at smc.vnet.net
• Subject: [mg34989] RE: [mg34976] How to compute a MatrixPower using: A^n = P D^n Inverse[P]
• From: "DrBob" <majort at cox-internet.com>
• Date: Tue, 18 Jun 2002 02:48:29 -0400 (EDT)
• Reply-to: <drbob at bigfoot.com>
• Sender: owner-wri-mathgroup at wolfram.com

```MatrixForm[A = {{3, 1, 0}, {1, 2, -1}, {0, -1, 3}}]
{evalues, evectors} = Eigensystem[A]
MatrixForm[ch = Transpose[evectors]]
Inverse[ch].A.ch // MatrixForm
MatrixForm[d = DiagonalMatrix[evalues]]
ch.d.Inverse[ch] == A

This only works when A has a basis of eigenvectors, of course.

Bobby Treat

-----Original Message-----
From: J. Guillermo Sanchez [mailto:guillerm at usal.es]
To: mathgroup at smc.vnet.net
Subject: [mg34989] [mg34976] How to compute a MatrixPower using: A^n = P D^n
Inverse[P]

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

```

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