一对称矩阵方程组解的研究

Research on the Solution to a System of Symmetric Matrix Equations

给出了四元数体上一对称矩阵方程组有斜埃尔米特解的充分必要条件,并得到了此方程组的斜埃尔米特解的一般表达式。应用主要结果讨论了四元数矩阵A和B矩阵有共同的斜埃尔米特广义逆的充要条件及斜埃尔米特广义逆的表示。

In this paper, we consider a system of matrix equations over quaternion algebra. Necessary and sufficient conditions for the existence and the expression of skew Hermitian solution to the system are derived. As an application, results for quaternion matrices and have a common skew Hermitian generalized inverse are obtained.