广义Schur补可逆的一些分块矩阵的Drazin逆表示  

Representations of the Drazin inverse of several block matrices with a nonsingular generalized Schur complement

作　　者：卜长江[1] 王光辉[1] 宋晓翠[1] 

机构地区：[1]哈尔滨工程大学理学院,黑龙江哈尔滨150001

出　　处：《哈尔滨工程大学学报》2012年第6期787-790,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)

摘　　要：分块矩阵的Drazin逆不仅在矩阵理论上被广泛研究而且在自动控制、广义系统、概率统计等方面有重要的应用.给出了当广义Schur补S=D-CADB可逆时,分块矩阵M=[AC BD] ∈Cn×n(A,D是方阵)在满足下列条件之一时的Drazin逆表示:1)BCAπ=O,BDCAπ=O,D2CAπ=O;2)CAπA2=O,CAπBC=O,CAπBD=O,CAπAB=O.这些结果推广了文献[9-10,12]的结论.The Drazin inverse of block matrices has been widely studied in matrix theory. It has important applications in automatic control, generalized systems, probability statistics, etc. In this paper, assuming that the generalized Schur complement S = D -CA^D B is nonsingular, the representations for the Drazin inverse of M=[A B C D]∈Cn×n were given （where A and D are square matrices） with the blocks satisfying one of the following conditions：l ） BCAπ =O,BDCAπ =O,D2CAπ =O;2 CAπA2 =O,CAπBC =O,CAπBD = ,CAπAB =O. These results generalize some known ones in [ 9-10,12 ].

关 键 词：DRAZIN逆 分块矩阵 广义SCHUR补 可逆矩阵 

分 类 号：O015.21[理学] TP273[自动化与计算机技术—检测技术与自动化装置]