On the computation of the nth power of a matrix
This is an incremental pedagogical note for mathematicians already familiar with linear algebra, offering no new insights or improvements.
The paper discusses computing the nth power of a matrix using the Cayley-Hamilton theorem and Gauss elimination for finding the minimum polynomial, but provides no concrete results or numbers.
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.