Asymptotic analysis of powers of matrices

Abstract

We analyze the representation of $A^n$ as a linear combination of $A^j,0\le j\le k-1,$ where $A$ is a $k\times k$ matrix. We obtain a first order asymptotic approximation of $A^n$ as $n\to \infty ,$ without imposing any special conditions on $A.$ We give some examples showing the application of our results.

14 pages