English

On the computation of the nth power of a matrix

Numerical Analysis 2017-05-16 v1

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.

Keywords

Cite

@article{arxiv.1705.04994,
  title  = {On the computation of the nth power of a matrix},
  author = {Nikolaos Halidias},
  journal= {arXiv preprint arXiv:1705.04994},
  year   = {2017}
}