The Sensitivity of the Matrix Exponential

Abstract

In this paper we examine how the matrix exponenetial $e^{At}$ is affected by perterbations in A. Elementary techniques using log norms and the Jordan and Schur factorizations indicate that $e^{At}$ is least sensitive when A is normal. Through the formulation of an exponential condition number, insight is gained into the connection between the condition of the eigensystem of A and the sensitivity of $e^{At}$.