m-weak group MP inverse

TL;DR

This paper introduces the m-weak group MP inverse, a new generalized matrix inverse that extends existing inverses and is useful for solving specific matrix equations.

Contribution

It presents the m-weak group MP inverse, unifying DMP-inverse and weak core inverse, along with its properties and applications.

Findings

Introduces the m-weak group MP inverse as a unifying generalized inverse.

Provides characterizations and representations of the new inverse.

Demonstrates applicability to solving restricted matrix equations.

Abstract

In this paper, we introduce a new matrix decomposition called the m-Core-nilpotent decomposition which is an extension of the Core-nilpotent decomposition. By this new decomposition, we propose a new generalized inverse named the m-weak group MP inverse which unifies the DMP-inverse and weak core inverse. Some characterizations, properties and representations of the m-weak group MP inverse are presented. In addition, the proposed generalized inverse is applicable to solving a restricted matrix equation.