哈尔滨工程大学学报2009，Vol.30Issue(10)：1185-1187,3.DOI:10.3969/j.issn.1006-7043.2009.10.019
体上一类具有幂等子块的分块矩阵的群逆
Group inverse of a class of block matrices with idempotent sub-blocks over skew fields
摘要
Abstract
Suppose K is a skew field and K~(n×n) is the set of all the n×n matrices over K. For A∈K~(n×n) if there exists a matrix X∈K~(n×n) satisfying the matrix equations AXA=A,XAX=X,AX=XA , then we call X the group inverse of A . Research on representations of the generalized inverses is an important problem in the theory of generalized inverses of matrices. The group inverse of block matrices has important applications in singular differential and difference equations, Markov chains, iterative methods, cryptography and so on. The existence and the representation of the block matrix [AB B0] (A,B∈K~(n×n),B~2=B,((I-B)A)~# wexists)are given in this paper.关键词
体/分块矩阵/幂等矩阵/群逆Key words
skew field/ block matrix/ idempotent matrix/ group inverse分类
数理科学引用本文复制引用
卜长江,郑兰,凌焕章..体上一类具有幂等子块的分块矩阵的群逆[J].哈尔滨工程大学学报,2009,30(10):1185-1187,3.基金项目
黑龙江省自然科学基金资助项目(159110120002). （159110120002）
