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.

Abstract

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.