On linear matrix differential equations

We use elementary methods and operator identities to solve linear matrix differential equations and we obtain explicit formulas for the exponential of a matrix. We also give explicit constructions of solutions of scalar homogeneous equations with certain initial values, called dynamic solutions, that play an important role in the solution of homogeneous and non-homogeneous matrix differential equations. We show that the same methods can be used to solve linear matrix difference equations. (c) 2006 Elsevier Inc. All rights reserved.