Remarks on computinge^{At}

Some points which have arisen in the author's attempts to teach Kirchner's method of computing e
^At
, where
A
is a real square matrix, to a class of undergraduate engineering students are discussed. These points include 1) how to avoid the one matrix inversion required, 2) how to handle pairs of complex eigenvalues, and 3) simplifications in the important case in which the eigenvalues are distinct.