Some new results on the core partial order
D. E. Ferreyra, Saroj B. Malik · Linear and Multilinear Algebra · 2020
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.