| 两个幂等矩阵的组合的群逆 |
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| 引用本文： | 左可正,谢涛.两个幂等矩阵的组合的群逆[J].数学杂志,2014,34(3):497-501. |
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| 作者姓名： | 左可正 谢涛 |
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| 作者单位： | 湖北师范学院数学与统计学院; |
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| 基金项目： | 湖北省教育厅重点项目(D20122202);湖北省教育厅青年项目(B20122203) |
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| 摘 要： | 本文研究了当P与Q是两个复数域上的n阶幂等矩阵且满足PQP=PQ时,组合aP+bQ+cP Q+dQP+eQP Q的群逆问题,利用矩阵的分块及群逆的性质,证明了它是群逆阵,并且给出了其群逆的表达式,其中ab=0,a,b,c,d,e为复数.
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| 关 键 词： | 群逆阵 幂等矩阵 组合 |
| 收稿时间： | 2012/3/5 0:00:00 |
| 修稿时间： | 2012/10/23 0:00:00 |
ON THE GROUP INVERSE OF COMBINATIONS OF TWOIDEMPOTENT MATRICES |
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| ZUO Ke-zheng and XIE Tao.ON THE GROUP INVERSE OF COMBINATIONS OF TWOIDEMPOTENT MATRICES[J].Journal of Mathematics,2014,34(3):497-501. |
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| Authors: | ZUO Ke-zheng and XIE Tao |
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| Institution: | School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China and School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China |
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| Abstract: | This paper studies the group inverse problem of the combination aP + bQ + cPQ + dQP + eQPQ, where P and Q are two idempotent matrices satisfying the condition PQP=PQ. By using the block decomposition of matrices and properties of group inverse, the combination is proved to be group invertible and the formulae of its group inverse is also obtained, where a, b, c, d, e are complex numbers with a, b nonzero. |
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| Keywords: | group inverse idempotent matrix combination |
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