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Journal of Applied Mathematics
Volume 2012 (2012), Article ID 471573, 19 pages
http://dx.doi.org/10.1155/2012/471573
Research Article

Constrained Solutions of a System of Matrix Equations

1Department of Mathematics, Shanghai University, 99 Shangda Road, Shanghai 200444, China
2Department of Basic Mathematics, China University of Petroleum, Qingdao 266580, China

Received 26 September 2012; Accepted 7 December 2012

Academic Editor: Panayiotis J. Psarrakos

Copyright © 2012 Qing-Wen Wang and Juan Yu. 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.

Abstract

We derive the necessary and sufficient conditions of and the expressions for the orthogonal solutions, the symmetric orthogonal solutions, and the skew-symmetric orthogonal solutions of the system of matrix equations and , respectively. When the matrix equations are not consistent, the least squares symmetric orthogonal solutions and the least squares skew-symmetric orthogonal solutions are respectively given. As an auxiliary, an algorithm is provided to compute the least squares symmetric orthogonal solutions, and meanwhile an example is presented to show that it is reasonable.