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arXiv · 1705.04994

On the computation of the nth power of a matrix

Nikolaos Halidias
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Abstract

In this note we discuss the problem of finding the nth power of a matrix which is strongly connected to the study of Markov chains and others mathematical topics. We observe the known fact (but maybe not well known) that the Cayley-Hamilton theorem is of key importance to this goal. We also demonstrate the classical Gauss elimination technique as a tool to compute the minimum polynomial of a matrix without necessarily know the characteristic polynomial.

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Nikolaos Halidias. 2017-05-14. On the computation of the nth power of a matrix. https://arxiv.org/abs/1705.04994

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