Computing the Minimum Polynomial, the Function and the Drazin Inverse of a Matrix with Matlab

Aims/ Objectives: In this note we will discuss the known (but not well known) problem of finding the minimum polynomial and the function of a matrix providing the simplest proofs for undergraduate students. We will try to explain with fairly simple arguments how to compute the minimum polynomial of a matrix giving also the matlab code for its symbolic computation. Next we will describe the (symbolic) computation of the matrix of a function via the Hermite interpolation method which seems to be the simplest method for undergraduate students. Finally we shall see how we can compute the Drazin inverse given the nth power of a matrix A.