Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

G-Drazin inverse combined with inner inverse

G. Maharanaa, J. K. Sahooa, Nestor Thome

Abstract

This paper introduces new classes of generalized inverses for square matrices named GD1, and the dual, called 1GD inverse. In addition, we discuss a few characterizations and representations of these inverses. The explicit expressions of these inverses have been established via core-nilpotent decomposition. Further, we introduce a binary relation for GD1 inverse and 1GD inverse, along with a few derived properties.

G-Drazin inverse combined with inner inverse

Abstract

This paper introduces new classes of generalized inverses for square matrices named GD1, and the dual, called 1GD inverse. In addition, we discuss a few characterizations and representations of these inverses. The explicit expressions of these inverses have been established via core-nilpotent decomposition. Further, we introduce a binary relation for GD1 inverse and 1GD inverse, along with a few derived properties.
Paper Structure (8 sections, 32 theorems, 10 equations)

This paper contains 8 sections, 32 theorems, 10 equations.

Table of Contents

  1. Introduction and background
  2. Preliminaries
  3. A brief recapitulation of generalized inverses
  4. GD1 inverse
  5. A binary relation based on GD1 inverses
  6. Computation of GD1 inverses by the core-nilpotent decomposition
  7. 1GD inverse
  8. A relation based on 1GD inverses

Key Result

Theorem 1.7

D1 Let $A, B \in\mathbb{C}^{n\times n}$ be matrices of index at most 1. If $A\leq ^{D,-}B$ then $A\leq \# B$.

Theorems & Definitions (46)

  • Definition 1.1
  • Definition 1.2
  • Definition 1.3
  • Definition 1.4
  • Definition 1.5
  • Definition 1.6
  • Theorem 1.7
  • Corollary 1.8
  • Definition 2.1
  • Example 2.2
  • ...and 36 more