Drazin invertibility for matrices over an arbitrary ring
نویسندگان
چکیده
منابع مشابه
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...
متن کاملEla 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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If a and b are elements of an algebra, then we show that ab is Drazin invertible if and only if ba is Drazin invertible. With this result we investigate products of bounded linear operators on Banach spaces. 1. Drazin inverses Throughout this section A is a real or complex algebra with identity e 6= 0. We denote the group of invertible elements of A by A. We call an element a ∈ A relatively reg...
متن کاملGeneralized Drazin invertibility of combinations of idempotents
The paper deals with the generalized Drazin invertibility of combinations of idempotents p, q in a Banach algebra. It proves the equivalence of the generalized Drazin invertibility of p−q and p+q, as well as the equivalence of the generalized Drazin invertibility of the commutator pq − qp and anticommutator pq + qp of p, q. It extends several results of J. Math. Anal. Appl. 359 (2009) 731–738, ...
متن کاملDrazin Invertibility of Product and Difference of Idempotents in a Ring
In this paper, several equivalent conditions on the Drazin invertibility of product and difference of idempotents are obtained in a ring. Some results in Banach algebras are extended to the ring case.
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2004
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(03)00618-9