| 分块矩阵的Drazin逆和平方幂零矩阵 |
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| 引用本文： | 庄礼斌.分块矩阵的Drazin逆和平方幂零矩阵[J].甘肃联合大学学报(自然科学版),2011,25(3):15-18. |
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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： | Campbell提出的寻找形如(ABC0)分块矩阵的广义逆的表达式的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(AA* A A 0),(AA* AA* A 0),(AA* A*A A 0),其中A为平方幂零矩阵,A*为A的共轭转置矩阵,利用Drazin逆和Moore-Penrose逆的关系及平方幂零矩阵性质,给出了这些分块矩阵的Dra-zin逆的表达式.
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| 关 键 词： | 分块矩阵 Drazin逆 平方幂零矩阵 |
Drazin Inverse of Some Special Partitioned Matrices and Square Nilpontent Matrix |
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| ZHUANG Li-bin.Drazin Inverse of Some Special Partitioned Matrices and Square Nilpontent Matrix[J].Journal of Gansu Lianhe University :Natural Sciences,2011,25(3):15-18. |
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| Authors: | ZHUANG Li-bin |
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| Institution: | ZHUANG Li-bin(School of Mathmatics and Computational Science,Guangdong University of Buziness Studies,Guangzhou 510320,China) |
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| Abstract: | Campbell discussed the problem of expressing the generalized inverse of a partitioned block matrix (A B C 0),but the problem has not been yet solved satisfactorily by scientists and researchers.We gives the following partitioned block matrices (AA* A A 0),(AA* AA* A 0),(AA* A*A A 0),where A is a square nilpontent matrix and A* is a transposed conjugate matrix of A,using formulas of Drazin inverses,Moore-Penrose inverses,and properties of square nilpontent matrix,the expressions of Drazin inverses of those partitioned block matrices are given. |
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| Keywords: | partitioned block matrix Drazin inverse square nilpontent matrix |
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