弱双四元数矩阵方程AXA^H+BYB^H=C的反Hermite解

On Anti-Hermitian Solutions of the Reduced Biquaternion Matrix Equation AXA^H+BYB^H=C

摘要: 在本文中，我们讨论弱双四元数矩阵方程AXA^H+BYB^H=C的反Hermite解，其中矩阵A,B是已知的弱双四元数矩阵，C是已知的弱双四元数反Hermite矩阵，X,Y是未知的弱双四元数反Hermite方阵。本文的目标是建立解存在的充分必要条件和通解表达式。

Abstract: In this paper, we discuss Anti-Hermitian solutions of reduced biquaternion matrix equation AXA^H+BYB^H=C , where A,B are known reduced biquaternion matrices with suitable size, C is a known reduced biquaternion anti-Hermitian matrix with suitable size, and X,Y are unknown re-duced biquaternion anti-Hermitian square matrices with suitable size. The objective of this paper is to establish a necessary and sufficient condition for the existence of a solution and a solution expression.