International Journal of Mathematics and Mathematical Sciences
Volume 2012 (2012), Article ID 307036, 19 pages
Research Article

The Real and Complex Hermitian Solutions to a System of Quaternion Matrix Equations with Applications

Department of Mathematics, East China University of Science and Technology, Shanghai 200237, China

Received 9 October 2011; Accepted 17 November 2011

Academic Editor: Qing-Wen Wang

Copyright © 2012 Shao-Wen 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.


We establish necessary and sufficient conditions for the existence of and the expressions for the general real and complex Hermitian solutions to the classical system of quaternion matrix equations A1X=C1,XB1=C2, and  A3XA3*=C3. Moreover, formulas of the maximal and minimal ranks of four real matrices X1,X2,X3, and X4 in solution X=X1+X2i+X3j+X4k to the system mentioned above are derived. As applications, we give necessary and sufficient conditions for the quaternion matrix equations A1X=C1,XB1=C2,A3XA3*=C3, and  A4XA4*=C4 to have real and complex Hermitian solutions.