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广义Schur补可逆的一些分块矩阵的Drazin逆表示

DOI: 10.3969/j.issn.1006-7043.201103079

Keywords: Drazin逆, 分块矩阵, 广义Schur补, 可逆矩阵

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Abstract:

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.本文给出了当广义Schur补S = D ? CADB 可逆时,分块矩阵M=[A B C D ]∈ Cmxn ( 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)CAπ A2 = O,CAπ BC = O, CAπ BD = O,CAπ AB = O .这些结果推广了文献[9-10,12]的结论.

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