| 关于某些特殊分块矩阵的群逆 |
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| 引用本文： | 卜长江,郑金山,赵杰梅.关于某些特殊分块矩阵的群逆[J].哈尔滨工程大学学报,2009,30(9). |
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| 作者姓名： | 卜长江 郑金山 赵杰梅 |
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| 作者单位： | 哈尔滨工程大学,理学院,黑龙江,哈尔滨,150001 |
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| 基金项目： | 黑龙江省自然科学基金资助项目 |
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| 摘 要： | 分块矩阵的广义逆不仅在数学理论上有广泛研究而且在自动控制、系统理论、概率统计、数学规划等领域有着广泛的实际研究背景.该文对形如A B/C 0]分块矩阵的群逆的表达式问题进行了研究.设P是复数域上的幂等阵.令矩阵A,B,C取自集合{P,PP*,PP*P },则可以得到27个形如A B/C 0]的分块矩阵.给出了这27个分块矩阵群逆的存在性与表示形式.
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| 关 键 词： | 群逆 Drazin逆 幂等矩阵 分块矩阵 |
The group inverse of some special block matrices |
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| BU Chang-jiang,ZHENG Jin-shan,ZHAO Jie-mei.The group inverse of some special block matrices[J].Journal of Harbin Engineering University,2009,30(9). |
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| Authors: | BU Chang-jiang ZHENG Jin-shan ZHAO Jie-mei |
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| Abstract: | Generalized inverses of block matrices are very useful in mathematical theory. They can also be applied in practices ranging from automated control systems, systems theory, probability statistics, mathematical programming and so on. Expressions for the group inverses of block matrices in the form of A B/C 0] were studied. Let P be an idempotent matrix over the field of complex numbers and matrices A,B,C be in the set {P,PP~* ,PP~*P} , we get 27 classes of block matrices in the form of A B/C 0] This paper gives the existence conditions and the expressions for the group inverses of the 27 classes of block matrices. |
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| Keywords: | group inverse Drazin inverse idempotent matrix block matrix |
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