Further results on the representation of the Drazin inverse of a 2×2 block matrix
Further results on the representation of the Drazin inverse of a 2×2 block matrix
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DOI：
10.1016/j.laa.2009.02.001
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发表时间：
2010-04
影响因子：
1.1
通讯作者：
Esther Dopazo;M. Martínez-Serrano
中科院分区：
文献类型：
--
作者：
Esther Dopazo;M. Martínez-Serrano
本文的目的是建立2×2块矩阵M=ABCD的Drazin逆的显式表示，其中a和D是方阵，用a和D的Drazin逆表示。首先，我们给出了块满足BC=0， BDC=0, BD2=0条件下M的Drazin逆的表达式。此外，我们推导了在较少限制条件下M的Drazin逆的表示，而不是在当前文献中发现的那些。
The aim of this paper is to establish an explicit representation of the Drazin inverse of a 2×2 block matrix M=ABCD, where A and D are square matrices, in terms of the Drazin inverses of A and D. First, we give a formula for the Drazin inverse of M with the blocks satisfying the conditions BC=0, BDC=0, and BD2=0. Further, we derive representations of the Drazin inverse of M under less restrictive conditions than those found in the current literature.