The W-weighted Drazin-star matrix and its dual

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Mengmeng Zhou
Jianlong Chen
Néstor Thome

Abstract

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

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