Core-EP Decomposition and its Applications

Abstract

In this paper, we introduce the notion of the core-EP decomposition and some of its properties. By using the decomposition, we derive several characterizations of the core-EP inverse, introduce a pre-order(i.e. the core-EP order) and a partial order(i.e. the core-minus partial order), and characterize the properties of both orders.

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• Representations and properties of the W-weighted core-EP inverse
• The core-EP inverse: A numerical approach for its acute perturbation
• The m-core-EP inverse in Minkowski space
• A new generalized inverse of matrices from core-EP decomposition
• *-DMP elements in $\ast$-semigroups and $\ast$-rings
• Simultaneous extension of generalized BT-inverses and core-EP inverses
• On generalized-Drazin inverses and GD-star matrices
• The core inverse and constrained matrix approximation problem
• m-weak group inverses in a ring with involution
• Determinantal representations of the weighted core-EP, DMP, MPD, and CMP inverses of matrices with quaternion and complex elements
• The quaternion core inverse and its generalizations
• Continuity of the core-EP inverse and its applications
• Weighted weak group inverse for Hilbert space operators
• Fuzzy linear systems and core-EP inverses