| 某些分块矩阵的Drazin逆和立方幂零矩阵 |
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| 引用本文： | 庄礼斌.某些分块矩阵的Drazin逆和立方幂零矩阵[J].贵阳金筑大学学报,2011(4):1-4. |
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| 作者姓名： | 庄礼斌 |
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| 作者单位： | 广东商学院数学与计算科学学院,广东广州510320 |
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| 摘 要： | S.L.Campbell在文献1]中提出的形如A B C 0]的分块矩阵的Drazin逆的表达式问题至今没有完全得到解决。本文对如下特殊情形的2×2分块矩阵A AA＊ AA＊ 0],AA＊ A A 0],其中A为立方幂零矩阵,A＊为A的共轭转置矩阵,利用Drazin逆和Moore-Penrose逆的关系及立方幂零矩阵性质,给出了这些分块矩阵的Drazin逆的表达式。
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| 关 键 词： | 分块矩阵 Drazin逆 立方幂零矩阵 |
Drazin Inverse of Some Special Partitioned Matrices and Cubic Nilpontent Matrix |
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| ZHUANG Li-bin.Drazin Inverse of Some Special Partitioned Matrices and Cubic Nilpontent Matrix[J].Journal of Jinzhu University of Guiyang,2011(4):1-4. |
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| Authors: | ZHUANG Li-bin |
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| Institution: | ZHUANG Li-bin (School of Mathematics and Computational Science,Guangdong University of Business Studies,Guangzhou 510320,China) |
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| Abstract: | Campbell discussed the problem of expressing the generalized inverse of a partitioned block matrixA B C 0],but the problem has not yet solved satisfactorily by scientists and researchers.Given the following partitioned block matrices A AA＊ AA＊ 0],AA＊ A A 0], where A is a cubic nilpontent matrix and A＊ is a transposed conjugate matrix of A,the expressions of Drazin inverses of those partitioned block matrices are given,by using formulas of Drazin inverses and Moore-Penrose inverses,and properties of cubic nilpontent matrix. |
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| Keywords: | partitioned block matrix Drazin inverse cubic nilpontent matrix |
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