Core EP, Dual Core EP and Composite Generalized Inverses for a Class of Structured Matrices

TL;DR

This paper develops explicit formulas and criteria for various generalized inverses, including core and dual core EP inverses, for matrices related to double star digraphs, enhancing understanding of their algebraic structure.

Contribution

It introduces new explicit formulas and existence criteria for multiple types of generalized inverses for matrices associated with double star digraphs.

Findings

Explicit block formulas for core and dual core EP inverses.

Existence criteria based on algebraic conditions.

Derived combined outer pseudoinverses with criteria.

Abstract

We study generalized inverses for matrices associated with double star digraphs. Explicit block formulas and existence criteria are obtained for core, dual core, core EP, and dual core EP inverses, expressed in terms of explicit algebraic criteria derived from the underlying block structure. Other combined outer pseudoinverses, combining Moore--Penrose and core-type inverses, are derived with existence criteria.