Dual Core-EP Generalized Inverse and Decomposition

TL;DR

This paper introduces the dual core-EP generalized inverse and dual core-EP decomposition for dual square matrices, analyzing their properties, relationships, and applications to solving inconsistent dual linear systems.

Contribution

It presents the first definition and analysis of the dual core-EP generalized inverse and dual core-EP decomposition, expanding the theory of dual matrix inverses.

Findings

Existence and uniqueness conditions for DCEPGI

Explicit formulas using dual Drazin and dual MP inverses

Applications to solving inconsistent dual linear systems

Abstract

In this work, we introduce a new type of generalized inverse called dual core-EP generalized inverse (in short DCEPGI) for dual square matrices. We analyze the existence and uniqueness of the DCEPGI inverse and its compact formula using dual Drazin and dual MP inverse. Moreover, some characterizations using core-EP decomposition are obtained. We present a new dual matrix decomposition named the dual core-EP decomposition for square dual matrices. In addition, some relationships with other dual generalized inverses are established. As an application, solutions to some inconsistent system of linear dual equations are derived.