Research Article

A generalization of the MP- m -WGI

Published in: Quaestiones Mathematicae
Volume 47 , issue 10 , 2024 , pages: 2133–2152

DOI: 10.2989/16073606.2024.2352566

Author(s): Dijana Mosić University 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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