Group inverse of modified matrices over an arbitrary ring
نویسندگان
چکیده
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.
منابع مشابه
Ela Group Inverse of Modified Matrices over an Arbitrary Ring
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...
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