منابع مشابه
Jacobson’s Lemma for Drazin Inverses
If a ring element α = 1 − ab is Drazin invertible, so is β = 1 − ba. We show that the Drazin inverse of β is expressible by a simple formula (in generalization of “Jacobson’s Lemma”) in terms of the Drazin inverse and the spectral idempotent of α. The commutation rules αa = a β and b α = β b are extended to the Drazin inverses, and the spectral idempotents of α and β are shown to be isomorphic....
متن کاملGroup Inverses and Drazin Inverses over Banach Algebras
For a matrix over a complex commutative unital Banach algebra, necessary and suucient conditions are given for the existence of its group inverse, and more generally, its Drazin inverses. The conditions are easy to check and explicit formulas for the inverses are provided. Some properties of the inverses and an application to operator theory are discussed. This note is a continuation of an earl...
متن کاملEla a Note on Newton and Newton–like Inequalities for M–matrices and for Drazin Inverses of M–matrices∗
In a recent paper Holtz showed that M–matrices satisfy Newton’s inequalities and so do the inverses of nonsingular M–matrices. Since nonsingular M–matrices and their inverses display various types of monotonic behavior, monotonicity properties adapted for Newton’s inequalities are examined for nonsingular M–matrices and their inverses. In the second part of the paper the problem of whether Draz...
متن کاملThe algorithm for computing the Drazin inverses of two-variable polynomial matrices
We propose a finite algorithm for computing Drazin inverse of two-variable polynomial matrices based on Greville s finite algorithm for computing Drazin inverse of a constant matrix. Also a three-dimensional recursive algorithm to do that is deduced. Examples show that these methods are feasible and the implementation is developed in the symbolic package MATLAB. 2002 Elsevier Inc. All rights re...
متن کاملSome additive results on Drazin inverses
In this paper, some additive results on Drazin inverse of a sum of Drazin invertible elements are derived. Some converse results are also presented.
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ژورنال
عنوان ژورنال: Operators and Matrices
سال: 2020
ISSN: 1846-3886
DOI: 10.7153/oam-2020-14-03