Electronic Journal of Differential Equations,
Vol. 2008(2008), No. 95, pp. 1-12.

Title: Linear matrix differential equations of higher-order and
       applications
  
Authors: Rajae Ben Taher (Univ. Moulay Ismail, Meknes, Morocco)
         Mustapha Rachidi (Academie de Reims, Morocco) 
 
Abstract: 
 In this article, we study linear differential equations
 of higher-order whose coefficients are square matrices.
 The combinatorial method for computing the matrix powers
 and exponential is adopted. New formulas representing
 auxiliary results are obtained. This allows us to prove
 properties of a large class of linear matrix differential
 equations of higher-order, in particular results of Apostol and
 Kolodner are recovered. Also illustrative examples and
 applications are presented.
 
Submitted February 25, 2007 Published July 05, 2008.
Math Subject Classifications: 15A99, 40A05, 40A25, 15A18.
Key Words: Algebra of square matrices; linear recursive relations; 
           matrix powers; matrix exponential;
	   linear matrix differential equations.