Theη-bihermitian solution to a system of real quaternion matrix equations
Zhuo‐Heng He, Qing‐Wen Wang · Linear and Multilinear Algebra · 2013
Let be the set of all matrices over the real quaternion algebra. , , , where is the conjugate of the quaternion . We call that is -Hermitian, if , ; is -bihermitian, if . We in this paper, present the solvability conditions and the general -Hermitian solution to a system of linear real quaternion matrix equations. As an application, we give the necessary and sufficient conditions for the systemto have an -bihermitian solution. We establish an expression of the -bihermitian to the system when it is solvable. We also obtain a criterion for a quaternion matrix to be -bihermitian. Moreover, we provide an algorithm and a numerical example to illustrate the theory developed in this paper.