Research Article

A generalization of the MP- m -WGI

Published in: Quaestiones Mathematicae
Volume 47 , issue 10, pages: 2133–2152

DOI: 10.2989/16073606.2024.2352566

Author(s): Dijana MosićUniversity of Niš, Serbia,

Keywords: 15A24, 15A09, 15A10, 65F05, MP--WGI, -WGI, inner inverse, 1WGI, MP weak group inverse,

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Abstract

Motivated by the notions of the MP--WGI and 1WGI, we further generalize these concepts and extend recent researches about them. Precisely, using an inner inverse and -WGI, we solve the system of matrix equation and introduce a new type of generalized inverses named the inner--WGI. The MP--WGI and 1WGI are known particular cases of inner--WGI, and inner-CEP and inner-GGI are special types of inner--WGI which present new generalized inverses in literature. We propose characterizations and formulae for the inner--WGI. A canonical matrix form of the inner--WGI is established. The -WG-inner inverse is defined and characterized as a dual inner--WGI. To solve some systems of linear equations and represent their general solutions, we apply the -WG-inner inverse and inner--WGI.

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Research Article

A generalization of the MP- m -WGI

Abstract

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