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Parametrizing $W$-weighted BT inverse to obtain the $W$-weighted $q$-BT inverse

D. E. Ferreyra, N. Thome, C. Torigino

Abstract

The core-EP and BT inverses for rectangular matrices were studied recently in the literature. The main aim of this paper is to unify both concepts by means of a new kind of generalized inverse called $W$-weighted $q$-BT inverse. We analyze its existence and uniqueness by considering an adequate matrix system. Basic properties and some interesting characterizations are proved for this new weighted generalized inverse. Also, we give a canonical form of the $W$-weighted $q$-BT inverse by means of the weighted core-EP decomposition.

Parametrizing $W$-weighted BT inverse to obtain the $W$-weighted $q$-BT inverse

Abstract

The core-EP and BT inverses for rectangular matrices were studied recently in the literature. The main aim of this paper is to unify both concepts by means of a new kind of generalized inverse called -weighted -BT inverse. We analyze its existence and uniqueness by considering an adequate matrix system. Basic properties and some interesting characterizations are proved for this new weighted generalized inverse. Also, we give a canonical form of the -weighted -BT inverse by means of the weighted core-EP decomposition.
Paper Structure (4 sections, 17 theorems, 51 equations)

This paper contains 4 sections, 17 theorems, 51 equations.

Table of Contents

  1. Introduction and preliminaries
  2. Existence and Uniqueness
  3. Algebraic characterizations
  4. Canonical form of the $W$-weighted $q$-BT inverse

Key Result

Lemma 2.1

Let $A\in {{\mathbb{C}}^{m\times n}}$ and $B\in {\mathbb{C}}^{n\times s}$. Then $P_B(AP_B)^\dag=(AP_B)^\dag$.

Theorems & Definitions (39)

  • Lemma 2.1
  • proof
  • Theorem 2.2
  • proof
  • Example 2.3
  • Definition 2.4
  • Remark 2.5
  • Corollary 2.6
  • proof
  • Remark 2.7
  • ...and 29 more