The $L^*$ Partial Order on the Set of Group Matrices

Abstract

In this paper, we use the Löwner partial order and the star partial order to introduce a new partial order (denoted by “$L^*$”) on the set of group matrices, and get some characteristics and properties of the new partial order. In particular, we prove that the $L^*$ partial order is a special kind of the core partial order and it is equivalent to the star partial order under some conditions. We also illustrate its difference from other partial orders with examples and find out under what conditions it is equivalent to other partial orders.