In this paper we study the W -weighted Drazin inverse of the bounded linear operators between Banach spaces and its representation theorem. Based on this representation, utilizing the spectral theory of Banach space operators, we derive an approximating expression of the W -weighted Drazin inverse and an error bound. Also, a perturbation theorem for the W -weighted Drazin inverse is uniformly o...

The Drazin inverse solutions of the matrix equations AX = B, XA = B and AXB = D are considered in this paper. We use both the determinantal representations of the Drazin inverse obtained earlier by the author and in the paper. We get analogs of the Cramer rule for the Drazin inverse solutions of these matrix equations and using their for determinantal representations of solutions of some differ...

After decades studying extensively two generalized inverses, namely Moore--Penrose inverse and Drazin inverse, currently, we found immersed in a new generation of inverses (core DMP etc.). The main aim this paper is to introduce investigate matrix related these defined for rectangular matrices. We apply our results the solution linear systems.

K e y w o r d s I n d e x , Drazin inverse, Group inverse, Per turbat ion bound, Core rank. 1. I N T R O D U C T I O N A necessary and sufficient condition for the continuity of the Drazin inverse (to be defined in the next section) was established by Campbell and Meyer in 1975 [1]. They stated the main result: suppose tha t Aj, j = 1, 2 , . . . , and A are n × n matrices such tha t A j ~ A . T...

Let A be a bounded linear operator on a Banach space such that the resolvent of A is rational. If 0 is in the spectrum of A, then it is well known that A is Drazin invertible. We investigate spectral properties of the Drazin inverse of A. For example we show that the Drazin inverse of A is a polynomial in A.

In this paper, we investigate an explicit representation of the generalized Drazin inverse (a ± b) d in terms of a, a d , b and b d under the condition ab = λba or ab = aba and extend to Banach algebras recent results of C.Y. Deng.

The purpose of this paper is to introduce a new generalized inverse, called DMP inverse, associated with a square complex matrix using its Drazin and Moore-Penrose inverses. DMP inverse extends the notion of core inverse, introduced by O.M. Baksalary and G. Trenkler for matrices of index at most 1 in [Core inverse of matrices, Linear and Multilinear Algebra, 2010, 681–697] to matrices of an arb...

In the linear system Ax = b the points x are sometimes constrained to lie in a given subspace S of column space of A. Drazin inverse for any singular or nonsingular matrix, exist and is unique. In this paper, the singular consistent or inconsistent constrained linear systems are introduced and the effect of Drazin inverse in solving such systems is investigated. Constrained linear system arise ...

In this paper we give representations of the Drazin and MP-inverse of a 2×2 block matrix and quotient identities for the generalized Schur complement of a partitioned 3 × 3 matrix under conditions different than those used in recent papers on the subject. We present numerical examples to illustrate our results. 2000 Mathematics Subject Classification: 15A09