Advanced Engineering Mathematics, 7th Edition

8.9 Powers of Matrices

INTRODUCTION

It is sometimes important to be able to quickly compute a power A^m, m a positive integer, of an n × n matrix A:

Of course, computation of A^m could be done with the appropriate software or by writing a short computer program, but even then, you should be aware that it is inefficient to simply use brute force to carry out repeated multiplications: A² = AA, A³ = AA², A⁴ = AAAA = A(A³) = A²A², and so on.

Computation of A^m

We are going to sketch an alternative method for computing A^m by means of the following theorem ...