Core–EP inverse

2013/04/29 by K. Manjunatha Prasad, K.S. Mohana, K. S. Mohana · 14 citations
Computer Science · #Matrix Theory and Algorithms

paper · doi:10.1080/03081087.2013.791690

Abstract

In this work, we introduce a notion of ‘core–EP inverse’ for a square matrix which is not essentially of index one. This extends the notion of ‘core inverse’, which was initially defined for the matrices of index one. The properties of matrices having ‘core–EP inverse’ and ‘core–EP generalized inverse’ are studied, and obtained a formula to compute the core–EP generalized inverse from a particular linear combination of minors of given matrix.

Citations

• Core inverse of matrices

Cited by

• Characterizations of the core inverse and the core partial ordering
• Weighted core–EP inverse of an operator between Hilbert spaces
• Further characterizations of the CMP inverse of matrices
• Characterizations of k-commutative equalities for some outer generalized inverses
• Common properties among various generalized inverses and constrained binary relations
• Pseudo core inverses in rings with involution
• Characterization and Representation of Weighted Core Inverse of Matrices
• Representations and properties of the W-weighted core-EP inverse
• Additive properties and absorption laws for generalized inverses
• A new generalized inverse of matrices from core-EP decomposition
• Weighted weak group inverse for Hilbert space operators
• The quaternion core inverse and its generalizations
• New properties of weighted generalized core-EP inverse in Banach algebras
• m-weak group inverses in a ring with involution

Related

• Core inverse of matrices
• The m-weak core inverse
• Generalized core inverses of matrices
• A new generalized inverse of matrices from core-EP decomposition
• On a new generalized inverse of matrices