摘要
1983年,Campbell提出了寻找形如A BC0的2×2分块矩阵广义逆表达形式的问题,至今没有得到完全解决.针对其特殊情形,即如下6个2×2分块矩阵,其中P为复数域上的立方幂等阵,P*为P转置共轭矩阵,运用群逆与{1}-逆的关系等式及群逆的一些性质研究了这6个分块矩阵群逆的存在性,并给出了相应的表达式.这些结果为研究的广义逆提供了一些思想借鉴,有助于进一步研究Campbell所提出的问题.
In 1983, Campbell discussed the problem of expressing the generalized inverse of a 2×2 partitioned block matrix[C 0 ^A B],but the problem has yet to be satisfactorily solved by scientists and researchers. Given the following six 2 × 2 partitioned blOck matrices [PP^＋ 0 ^P P],[P^＊ 0 ^P P],[PP^＊ 0 ^P PP^＊],[P^＊ 0 ^P PP^＊],[P 0^PP^＊ PP^＊],[P 0 ^PP^＊ P],where P is a given tripotent matrix over the field of complex numbers, and P^＊ is a transposed conjugate matrix of P. The existence of group inverses of these six 2×2 partitioned block matrices are given by using formulas of group inverse and {1}- inverse and properties of group inverses, and the related expressions are given. These results offer some ideas for finding the generalized inverse of [C 0 ^A B],suggesting there is a solution to Campbell＇s problem.
出处
《哈尔滨工程大学学报》
EI
CAS
CSCD
北大核心
2008年第5期529-532,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
分块矩阵
群逆
立方幂等阵
partitioned matrix
group inverse
tripotent matrix
