A generalization of the MP-m-WGI

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.

Mathematics Subject Classification (2020):

• 15A24
• 15A09
• 15A10
• 65F05

Key words:

• MP--WGI
• -WGI
• inner inverse
• 1WGI
• MP weak group inverse