Some new results on the core partial order. Issue 18 (12th December 2022)

• Record Type: Journal Article
• Authors: Ferreyra, D. E.; Malik, Saroj B.
• Is Part Of: Linear & multilinear algebra. Volume 70:Issue 18(2022)
• Page Start: 3449
• Page End: 3465
• Publication Date: 2022-12-12
• Subjects: Core partial order -- diamond partial order -- sharp partial order -- minus partial order -- core inverse -- group inverse -- Moore–Penrose inverse -- EP matrix; Primary: 15A09 -- Secondary: 06A06; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2020.1841078
• Languages: English
• ISSNs: 0308-1087

Abstract

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.