Matrix Exponentials---Another Approach

Abstract

Abstract. The exponential of a matrix and the spectral decomposition of a matrix can be computed knowing nothing more than the eigenvalues of the matrix and the Cayley-Hamilton theorem. The arrangement of the ideas in this paper is simple enough to be taught to beginning students of ODEs.

Functions of matrices

“…Some interesting recent papers on the subject are [10,13]. The classical approaches are presented in [12,16,9].…”

Remarks on the Calculation of the Power of a Matrix

“…It is obvious that for both cases the Jordan canonical form of the matrix A can be employed. However, alternative and pedagogically simpler methods based on the Cayley -Hamilton theorem were recently proposed: for the differential case by Putzer [10], Leonard [9] and Harris-Fillmore -Smith [3]; for the difference case by LaSalle [8], Kwapisz [6] and Elaydi -Harris [2].…”

On a Recursion Formula Related to Confluent Vandermonde

“…Moreover, an important application of the confluent Vandermonde matrix and its inverse is to evaluate the state transition matrix of linear invariant systems or, in short, the matrix exponential. In this connection, see [14], [15], [16], [17] for more details and explanations.…”