关于2×2分块矩阵的Drazin逆的一般表达式(英文)  

A new representation for the Drazin inverses of 2×2 block matrices

作　　者：顾旸旸[1] 许庆祥[1] 

机构地区：[1]上海师范大学数理学院,上海200234

出　　处：《上海师范大学学报（自然科学版）》2009年第3期249-252,共4页Journal of Shanghai Normal University(Natural Sciences)

基　　金：supported by Innovation Program of Shanghai Municipal Education Commission(09YZ147);Shanghai Normal University Fund(DYL901)

摘　　要：1979年,Campbell和Meyer就提出:希望找到一个公式研究求解2×2分块矩阵M=[ABCD]的Drazin逆这个问题,其中A和D必须是方阵.受Drangana S.Cvekovic-Ilic近期关于2×2分块矩阵的Drazin逆表示的启发,提出在特定条件下2×2分块矩阵的Drazin逆的一般表达式.继而给出一个例子以证明结论的正确性.In 1979, Campbell and Meyer proposed the problem of finding a formula for the Drazin inverse of general 2 × 2 matrix M =（A B C D） in terms of its various blocks, where the blocks A and D are required to be square matrices. Special cases of the problem have been studied intensely. Inspired by the recent work of Dragana S. Cvetkovic - Ilic. We give a new representation for the Drazin inverse of 2 × 2 block matrix under certain conditions.

关 键 词：分块矩阵 DRAZIN逆 Drazin指标 

分 类 号：O177.5[理学—数学]