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