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Journal of Applied Mathematics
Volume 2013, Article ID 537520, 7 pages
Research Article

Necessary and Sufficient Conditions for the Existence of a Positive Definite Solution for the Matrix Equation

Department of Mathematics, Faculty of Science, Menoufia University, Shebin El-Koom, Egypt

Received 19 December 2012; Revised 26 March 2013; Accepted 14 May 2013

Academic Editor: Theodore E. Simos

Copyright © 2013 Naglaa M. El-Shazly. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this paper necessary and sufficient conditions for the matrix equation to have a positive definite solution are derived, where , is an identity matrix, are nonsingular real matrices, and is an odd positive integer. These conditions are used to propose some properties on the matrices , . Moreover, relations between the solution and the matrices are derived.