| 一对称矩阵方程组解的研究 |
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| 引用本文： | 江静,马燕,蓝海波.一对称矩阵方程组解的研究[J].山东教育学院学报,2011,26(5):109-111. |
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| 作者姓名： | 江静 马燕 蓝海波 |
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| 作者单位： | 1. 齐鲁师范学院数学系,山东济南,250013
2. 即墨市实验高级中学,山东即墨,266200 |
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| 摘 要： | 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。
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| 关 键 词： | 四元数 矩阵方程组 斜埃尔米特解 广义逆． |
Research on the Solution to a System of Symmetric Matrix Equations |
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| Jiang Jing Ma Yan Lan Haibo.Research on the Solution to a System of Symmetric Matrix Equations[J].Journal of Shandong Education Institute,2011,26(5):109-111. |
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| Authors: | Jiang Jing Ma Yan Lan Haibo |
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| Institution: | Jiang Jing Ma Yan Lan Haibo (1. Department of Mathematics, Qilu Normal University,Jinan 250013, China; 2. Experimental High School of Jimo, Jimo 266200, China) |
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| Abstract: | 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. |
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| Keywords: | Quaternion A system of matrix equations Skew Hermitian solution Generalized inverse |
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