The representation of the Drazin inverse of anti-triangular operator matrices based on resolvent expansions
The representation of the Drazin inverse of anti-triangular operator matrices based on resolvent expansions
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DOI：
10.1016/j.amc.2014.05.053
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发表时间：
2014-09
期刊：
影响因子：
--
通讯作者：
Junjie Huang;Yunfeng Shi;Alatancang Chen
中科院分区：
文献类型：
--
作者：
Junjie Huang;Yunfeng Shi;Alatancang Chen
研究了反三角算子矩阵M= A B C 0，其中A2 = A，CA π B= 0.利用预解式展开技术，我们得到了M的Drazin逆的显式表示，即M的Drazin逆的元素和元素的Drazin逆及其组合.所得结果推广了Bu等的主要结果.（2011）[2]和Castro-González和Dopazo（2005）[6]以及Bu et al.（2008）[3]和Liu和Yang（2012）[14]。作为应用，给出了两个矩阵P，Q∈ Cn × n（P2 = P，PQ 2= 0）的Drazin逆的一个新的可加性结果.
This paper deals with the anti-triangular operator matrix M= A B C 0 with A 2= A and CA π B= 0. Using the resolvent expansion technique, we obtain the explicit representation of the Drazin inverse of M, in terms of its entries and the Drazin inverses of the entries and their compositions. The result extends the main results in Bu et al.(2011)[2] and Castro-González and Dopazo (2005)[6] and the results on group inverses in Bu et al.(2008)[3] and Liu and Yang (2012)[14]. As an application, a new additive result is given of the Drazin inverse for two matrices P, Q∈ C n× n with P 2= P and PQ 2= 0.