关于2×2分块矩阵的Drazin逆的一般表达式

摘要

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.%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=(A B C D)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.