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International Journal of Mathematics and Mathematical Sciences
Volume 2006, Article ID 79617, 12 pages

Asymptotic analysis of powers of matrices

Department of Mathematics, State University of New York at New Paltz, 75 S. Manheim Boulevard, Suite 9, New Paltz 12561-2443, NY, USA

Received 13 September 2005; Revised 28 May 2006; Accepted 30 May 2006

Copyright © 2006 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We analyze the representation of An as a linear combination of Aj, 0jk1, 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.