The g-Drazin inverses of special operator matrices

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....

The explicit representations of the Drazin inverses of a class of block matrices

Ela the Explicit Representations of the Drazin Inverses of a Class of Block Matrices

Let M = A B C D be a 2 × 2 block matrix, where ABC = 0 and either DC = 0 or BD = 0. This paper gives the explicit representations of M D in terms of A, B, C, D, A D , (BC) D and D D .

The 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...

Group 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...