Journal of Mathematical Sciences: Advances and Applications Volume 1, Number 2, 2008, Pages 373-387 2000 Mathematics Subject Classification: 15A24, 15A69, 44A35. Keywords and phrases: matrix products, coupled matrix differential equations, diagonal extraction operator. Received April 14, 2008  2008 Scientific Advances Publishers A COMPUTATIONALLY-EFFICIENT SOLUTIONS OF COUPLED MATRIX DIFFERENTIAL EQUATIONS FOR DIAGONAL UNKNOWN MATRICES ZEYAD AL ZHOUR Department of Mathematics Faculty of Science and Information Technology Zarqa Private University (ZPU) P. O. Box 2000 Zarqa 1311, Jordan e-mail: zeyad1968@yahoo.com Abstract In the present paper, we present a simple and effective method to produce solutions to the coupled matrix linear differential equations based on the Hadamard product of matrices. The analysis indicates that the Hadamard structure method can achieve good efficient when the unknown matrices are diagonal. Several matrix systems can be solved by the new approach as a special case. 1. Introduction and Preliminary Results Coupled matrix differential equations have been widely used in stability theory of differential equations, control theory, communication systems, perturbation analysis and other fields of pure and applied mathematics; and also recently in the context of the analysis and numerical simulation of descriptor systems. For instance, the canonical system