摘要
1979年,Campbell和Meyer提出了求2×2分块矩阵[A B C D]的Drazin逆(群逆)表达式问题,这里A和D是方阵.即使当D=0,此问题仍未解决.设K是一个体,Kn×n表示K上所有n×n矩阵的全体.这里主要给出了体上分块矩阵[AA#AB0](A,B∈Kn×n)群逆存在的充分必要条件及其具体表达式.
In 1979, Campbell and Meyer proposed a problem： finding an explicit expression of the Drazin （group） inverse for the 2 × 2 block matrix [A B C D] , where A and D are square matrices. Until now this problem has not been solved even in the case of D = 0. Let K be a skew field, Kn^n ×n be the set of all n × n matrices over K. The purpose of this paper is to give necessary and sufficient conditions for the existence as well as the expression of the group inverse for the block matrix [AA^#A B 0 ] ,where A,B∈K^n×n .
出处
《哈尔滨工程大学学报》
EI
CAS
CSCD
北大核心
2010年第3期405-408,共4页
Journal of Harbin Engineering University
基金
黑龙江省自然科学基金资助项目(159110120002)
关键词
体
群逆
分块矩阵
skew fields
group inverse
block matrix
