The matrix exponential can be found in various connections in analysis and control of dynamic systems. In this short note we are going to list a few examples. The matrix exponential usably pops up in connection to the sampling process, whatever it is in a deterministic or a stochastic setting or it is a tool for determining a Gramian matrix. This note is intended to be used in connection to the teaching post the course in Stochastic Adaptive Control (02421) given at Informatics and Mathematical Modelling (IMM), The Technical University of Denmark. This work is a result of a study of the litterature.