The η-Hermitian solutions to some systems of real quaternion matrix equations

Abstract

Let Hmxn be the set of all m x n matrices over the real quaternion algebra. We call that A ? Hnxn is ?-Hermitian if A = A?* where A?* = -?A*?,? ? {i,j,k},i,j,k are the quaternion units. In this paper, we derive some solvability conditions and the general solution to a system of real quaternion matrix equations. As an application, we present some necessary and sufficient conditions for the existence of an ?-Hermitian solution to some systems of real quaternion matrix equations. We also give the expressions of the general ?-Hermitian solutions to these systems when they are solvable. Some numerical examples are given to illustrate the results of this paper.