A Study of the Matrix Exponential
Van Loan, F Charles · 2006
This report brings together a wide variety of facts concerning the matrix exponential. Against a background of familiar results, we present an analysis of matrix functions (the exponential in particular) which exploits the Schur decomposition theorem. This helps us explore the behavior of a function of a matrix whose eigensystem is poorly conditioned. Finally, we investigate Pade approximation of the matrix exponential and feature in the discussion a potentially useful inverse error analysis.