International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Issue 14, Article ID 79617, 12 pages
doi:10.1155/IJMMS/2006/79617
Asymptotic analysis of powers of matrices
Diego Dominici
Department of Mathematics, State University of New York at New Paltz, 75 S. Manheim Boulevard, Suite 9, New Paltz 12561-2443, NY, USA
Abstract
We analyze the representation of An as a linear combination of Aj, 0≤j≤k−1, where A is a k×k matrix. We obtain a first-order asymptotic approximation of An as n→∞, without imposing any special conditions on A. We give some examples showing the application of our results.