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.
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.
出处
《甘肃联合大学学报（自然科学版）》
2011年第3期15-18,共4页
Journal of Gansu Lianhe University :Natural Sciences
关键词
分块矩阵
DRAZIN逆
平方幂零矩阵
partitioned block matrix
Drazin inverse
square nilpontent matrix
