Further results for the dual Hartwig-Spindelb{\"o}ck decomposition and its applications

TL;DR

This paper introduces new forms of the dual Hartwig-Spindelb{"o}ck decomposition, providing explicit representations for dual generalized inverses and exploring their properties, relationships, and applications in dual matrix analysis.

Contribution

It presents two novel dual Hartwig-Spindelb{"o}ck decompositions and applies them to characterize dual generalized inverses and dual partial orders.

Findings

Explicit representations for classes of dual generalized inverses

Characterization of dual composite generalized inverses

Verification of dual partial order applicability

Abstract

In this paper, we introduce two new forms of the dual Hartwig-Spindelb{\"o}ck decomposition and employ them to derive explicit representations for several classes of dual generalized inverses. Building on these representations, we further explore and characterize the relationships and properties of these inverses, investigate the dual composite generalized inverses, and verify the applicability of dual partial orders. The proposed decomposition provides a systematic and convenient framework for the study of dual matrices.