Group inverse of modified matrices over an arbitrary ring
Group inverse of modified matrices over an arbitrary ring
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DOI：
10.13001/1081-3810.1650
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发表时间：
2013
影响因子：
0.7
通讯作者：
N. Castro-González
中科院分区：
文献类型：
--
作者：
N. Castro-González
本文主要研究修正矩阵M = A-BC的群逆，其中A是一个n×n矩阵，其元素在任意一个有单位元的环R中，B，n×k和C，k×n是元素在R中的矩阵.我们假设A有群逆，并给出了保证M的群逆存在的条件。本文给出了M的群逆的Sherman-Morrison-伍德伯里公式的一个推广。一些特殊的情况下，所获得的结果和应用进行了讨论。
We focus on the group inverse of modified matrices M = A−BC, where A is an n×n matrix with entries in an arbitrary ring R with unity and B, n×k, and C, k×n, are matrices having entries in R. We assume that A has the group inverse and we give conditions that guarantee the existence of the group inverse of M . We present an extension of the Sherman-Morrison-Woodbury formulae for the group inverse of M . Some particular cases and applications of the results obtained are discussed.