Hermitian Solutions to a Quaternion Matrix Equation
In this paper, we consider Hermitian and skew-Hermitian solutions to a certain matrix equation over quaternion algebra H. Necessary and sufficient conditions are obtained for the quaternion matrix equation to have Hermitian and skew-Hermitian solutions, and the expressions of such solutions are also given. As an application, the common skew-Hermitian g-inverse of quaternion matrix A and B is considered.
Shaobo Zhong, Yimin Cheng and Xilong Qu
N. Li et al., "Hermitian Solutions to a Quaternion Matrix Equation", Applied Mechanics and Materials, Vols. 50-51, pp. 391-395, 2011