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Evaluating a polynomial on a matrix; matrix computations over a finite field

• To: mathgroup at smc.vnet.net
• Subject: [mg43123] Evaluating a polynomial on a matrix; matrix computations over a finite field
• From: Lot-o-fun <lotofun at hotmail.com>
• Date: Wed, 13 Aug 2003 07:49:54 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

How do I compute p(A), where p is a polynomial and A is a matrix?

For example, if

p[x_] := x^2 - 3x + 2

and

A = {{1,2},{3,4}}, then I want to compute

p(A) = A^2 - 3A + 2I = {{6,4},{6,12}}

Is there some way of doing this?

I'd also like to be able to do various matrix computations over finite
fields.  For example, I'd like to compute the minimal polynomial of a
matrix over Z_2.

Thanks!

-Lotofun

• Follow-Ups:
  • Re: Evaluating a polynomial on a matrix; matrix computations over a finite field
    • From: Daniel Lichtblau <danl@wolfram.com>