| 一个四元数矩阵方程组的η-Hermitian解 |
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| 引用本文： | 陈笛,吴维峰.一个四元数矩阵方程组的η-Hermitian解[J].上海大学学报(自然科学版),2013,19(6):606-610. |
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| 作者姓名： | 陈笛 吴维峰 |
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| 作者单位： | 1. 上海大学 理学院, 上海 200444; 2. 潍坊工程职业学院 会计与统计学院, 山东 潍坊 262500 |
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| 基金项目： | 国家自然科学基金资助项目(11171205); 上海市教委创新基金资助项目(13ZZ080) |
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| 摘 要： | 对于四元数矩阵方程组AXAη∗+ BYBη∗= E, CYCη∗+ DZDη∗= F , 首先运用 4 个矩阵的奇异值分解, 给出四元数矩阵方程组有η-Hermitian解的充要条件; 然后, 利用该充要条件给出矩阵方程组η-Hermitian解的表达式.
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| 关 键 词： | 矩阵分解 四元数矩阵 秩 |
η-Hermitian Solutions to a System of Quaternion Matrix Equations |
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| CHEN Di,WU Wei-feng.η-Hermitian Solutions to a System of Quaternion Matrix Equations[J].Journal of Shanghai University(Natural Science),2013,19(6):606-610. |
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| Authors: | CHEN Di WU Wei-feng |
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| Institution: | 1. College of Sciences, Shanghai University, Shanghai 200444, China;2. Accounting and Statistics School of Mathematics,Weifang Engineering Vocational College, Weifang 262500, Shandong, China |
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| Abstract: | This paper derives a necessary and sufficient condition for the existence of the η-Hermitian solutions to the quaternion matrix equationsAXAη∗+ BYBη∗= E, CYCη∗+ DZDη∗= F by using the singular value decomposition of four matrices, and gives an expression of the η-Hermitian solutions to the quaternion matrix equations. |
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| Keywords: | matrix decomposition quaternion matrix rank |
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