On the Computation of the Minimum Polynomial and Applications
Nikolaos Halidias *
Department of Statistics and Actuarial-Financial Mathematics, University of the Aegean, Karlovassi 83200 Samos, Greece.
*Author to whom correspondence should be addressed.
Abstract
Aims/Objectives: In this review article we study the computation of the minimum polynomial
of a matrix A and how we can use it for the computation of the matrix An. We also describe
the form of the elements of the matrix A-n and we will see that it is closely related with the
computation of the Drazin generalized inverse of A. Next we study the computation of the
exponential matrix and nally we give a simple proof of the Leverrier - Faddeev algorithm for
the computation of the characteristic polynomial.
Keywords: Minimum polynomial, characteristic polynomial, exponential matrix, Drazin inverse, Leverrier - Faddeev algorithm