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In this paper, we revise the core EP inverse of a square matrix introduced by Prasad and Mohana in [Core EP inverse, Linear and Multilinear Algebra, 62 (3) (2014) 792-802]. Firstly, we give a new representation and a new characterization of the core EP inverse. Then, we study some properties of the core EP inverse by using a representation by block matrices. Secondly, we extend the notion of core EP inverse to rectangular matrices by means of a weighted core EP decomposition. Finally, we study some properties of weighted core EP inverses.

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“…is called the DMP inverse of A and is denoted by A d, † . For some related results we refer the reader to [5,9,11].…”

Section: Introductionmentioning

confidence: 99%

Revisiting the core EP inverse and its extension to rectangular matrices

Ferreyra

Levis

Thome

2017

Quaestiones Mathematicae

108

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“…For a most extensive study on generalized inverses, matrix partial orders, and pre-orders the authors refer the reader to [1,2,3,6,7,10,12,13,14,18,19,20,21,22,24,26].…”

Section: Definition 14mentioning

confidence: 99%

Weighted G-Drazin inverses and a new pre-order on rectangular matrices

Coll

Lattanzi

Thome

2018

Applied Mathematics and Computation

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This paper deals with weighted G-Drazin inverses, which is a new class of matrices introduced to extend (to the rectangular case) G-Drazin inverses recently considered by Wang and Liu for square matrices. First, we define and characterize weighted G-Drazin inverses. Next, we consider a new pre-order defined on complex rectangular matrices based on weighted G-Drazin inverses. Finally, we characterize this pre-order and relate it to the minus partial order and to the weighted Drazin pre-order.

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“…However, to our acknowledge, the minus partial order for nilpotent matrices has not been investigated and it will be partially considered in this paper. In [8,9] similar relations to Drazin preorder were studied for rectangular matrices, and then extended to operators on Banach spaces in [4,11].…”

Section: Introductionmentioning

confidence: 99%