Common properties among various generalized inverses and constrained binary relations

2022/04/12 by Ruifei Kuang, Chunyuan Deng · 1 citation
Computer Science · Physics and Astronomy · Mathematics · #Matrix Theory and Algorithms #Electromagnetic Scattering and Analysis #Iterative Methods for Nonlinear Equations

paper · doi:10.1080/03081087.2022.2061399

Abstract

The common characterizations and various individual properties of different generalized inverses are established. Several equivalent conditions for the core-EP, weak group inverse, m-weak group inverse and weak core inverse are presented. The brand new explicit expressions for the operator binary relations defined by various generalized inverses are obtained. We derive properties and study the relationship between two different elements A,B∈B(H) and their (T,S)-outer generalized inverses AT,S(2) and BT,S(2) through which the reverse order law results about (AB)◯w=B◯wA◯w and (AB)◯d=B◯dA◯d are obtained.

Citations

• Core inverse of matrices
• Core–EP inverse
• Pseudo-Inverses in Associative Rings and Semigroups
• On a new generalized inverse of matrices
• Characterizations of k-commutative equalities for some outer generalized inverses
• Some new results on the core partial order

Cited by

• Generalized right group inverse in Banach *-algebras

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