Some new results on the core partial order. Issue 18 (12th December 2022) - Ferreyra, D. E.; Malik, Saroj B.
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.