Core inverse of matrices

2009/11/06 by Oskar Maria Baksalary, Götz Trenkler · 32 citations
Computer Science · Physics and Astronomy · #Matrix Theory and Algorithms #Electromagnetic Scattering and Analysis #Scientific Research and Discoveries

paper · doi:10.1080/03081080902778222

Abstract

This article introduces the notion of the Core inverse as an alternative to the group inverse. Several of its properties are derived with a perspective towards possible applications. Furthermore, a matrix partial ordering based on the Core inverse is introduced and extensively investigated.

Cited by

• Hyper-dual group inverse: existence, characterizations, and applications
• Core–EP inverse
• Characterizations of the core inverse and the core partial ordering
• Some new results on the core partial order
• Weighted core–EP inverse of an operator between Hilbert spaces
• The class of<i>m</i>-<i>EP</i>and<i>m</i>-normal matrices
• Further characterizations of the CMP inverse of matrices
• New results on (<i>b</i>, <i>c</i>)–inverses
• On a new generalized inverse of matrices
• On Drazin-Moore-Penrose inverses of finite potent endomorphisms
• Characterizations of <i>k</i>-commutative equalities for some outer generalized inverses
• Core and strongly core orthogonal matrices
• Common properties among various generalized inverses and constrained binary relations
• Weighted pseudo core inverses in rings
• Partial orders based on core-nilpotent decomposition
• Pseudo core inverses in rings with involution
• On a weighted core inverse in a ring with involution
• New partial orders on Rickart *-rings
• The minus order and range additivity
• Characterization and Representation of Weighted Core Inverse of Matrices
• Representations and properties of the W-weighted core-EP inverse
• Orthogonal tripotent matrices
• Dual DMP generalized inverses of dual matrices and their applications in linear dual equations
• On the continuity and differentiability of the (dual) core inverse in C*-algebras
• Revisiting generalized inverses of a sum with a radical element
• Core partial order in rings with involution
• New characterizations for core inverses in rings with involution
• New characterizations of weak CMP inverses
• *-DMP elements in *-semigroups and *-rings
• Additive properties and absorption laws for generalized inverses
• EP elements in rings with involution
• Determinantal representations of the weighted core-EP, DMP, MPD, and CMP inverses of matrices with quaternion and complex elements

Related

• Generalized core inverses of matrices
• Core–EP inverse
• The m-weak core inverse
• Characterization and Representation of Weighted Core Inverse of Matrices
• Characterizations of the core inverse and the core partial ordering