© 2015 The Franklin Institute. Published by Elsevier Ltd. All rights reserved. In this paper, we present a solution of general dynamic matrix linear systems based on operator theory. For general linear operators defined in matrix form the concept of operator exponential functions is first proposed, and some properties are then established. With the proposed operator exponential functions as a tool, the solution to general matrix linear systems is derived. Furthermore, by using the obtained results on dynamic matrix systems, the solution of a class of general linear matrix equations is expressed in the form of infinite integration.