Some new results on the core partial order

2020/11/03 by D. E. Ferreyra, Saroj B. Malik · 2 citations
Computer Science · Mathematics · Engineering · #Matrix Theory and Algorithms #Advanced Topics in Algebra #graph theory and CDMA systems

paper · doi:10.1080/03081087.2020.1841078

Abstract

The current research investigates the core partial order for its further properties. We introduce a new property for matrices of index at most 1, namely (B−A)◯#=B◯#−A◯# and is called as ‘the core-subtractivity’. This property then is used to explore relations between the powers and subtractivity properties of the core partial order. In particular, we prove that A≤◯#B is equivalent to (B−A)≤◯#B under the core-subtractivity property. We also examine some new conditions under which the core partial order is equivalent to the minus and diamond partial orders.

Citations

• Core inverse of matrices
• Characterizations of the core inverse and the core partial ordering

Cited by

• Core and strongly core orthogonal matrices
• Common properties among various generalized inverses and constrained binary relations

Related

• Core inverse of matrices
• Characterizations of the core inverse and the core partial ordering
• New characterizations of the diamond partial order
• A new class of partial orders
• Core and strongly core orthogonal matrices