Matrix Power, Determinant and Polynomials

Abstract

Commonly used approaches to calculating large matrix powers require the eigenvalues of matrices, and often eigenvalue computation can become a demanding and tedious work [3]. Abu-Saris and Ahmad provided in their paper [1] an approach that makes use of polynomials to calculate large powers of matrices. Their approach does not require eigenvalue calculation. The approach begins with the characteristic polynomial of square matrices, and continues with the use of the division algorithm along with the application of Cayley-Hamilton Theorem [2, p.210]. This approach produces a recursive algorithm for the computation of the coefficients of polynomials [1].