Characterizations of the core inverse and the core partial ordering

2014/10/27 by Hongxing Wang, Xiaoji Liu · 5 citations
Computer Science · Mathematics · #Matrix Theory and Algorithms #Advanced Optimization Algorithms Research #Advanced Topics in Algebra

paper · doi:10.1080/03081087.2014.975702

Abstract

In this note, we revisit the core inverse and the core partial ordering introduced by Baksalary and Trenkler [Linear Multilinear Algebra. 2010;58:681–697]. We prove that the core inverse of is the unique solution of and , and establish several characterizations of the core inverse, the core partial ordering and the reverse order law for the core inverse.

Citations

• Core inverse of matrices
• Core–EP inverse

Cited by

• Some new results on the core partial order
• The class of<i>m</i>-<i>EP</i>and<i>m</i>-normal matrices
• Characterizations of <i>k</i>-commutative equalities for some outer generalized inverses
• Partial orders based on core-nilpotent decomposition
• Characterization and Representation of Weighted Core Inverse of Matrices

Related

• Core inverse of matrices
• Some new results on the core partial order
• A new class of partial orders
• Reverse-order law for core inverse of tensors
• On forward-order law for core inverse in rings