The W-weighted m-weak group MP inverse and its applications

TL;DR

This paper introduces the W-weighted m-weak group MP inverse, a new generalized inverse for rectangular matrices, unifying existing inverses and demonstrating applications in optimization and matrix equations.

Contribution

It extends the m-weak group MP inverse to rectangular matrices, unifies several inverse concepts, and explores their properties and applications.

Findings

Unified the W-weighted weak core and DMP inverses

Derived properties and representations of the new inverse

Applied the inverse to solve constrained optimization and matrix equations

Abstract

We extend the concept of the m-weak group MP inverse of a square matrix to a rectangular matrix, called the W-weighted m-weak group MP inverse, which also unifies the W-weighted weak core inverse and W-weighted DMP inverse. Some properties, characterizations and representations of this new generalized inverse are shown. Additionally, applications of the W-weighted weak group MP inverse are given in solving a constrained optimization problem and a class of consistent matrix equations.