Ordered matrices with nonnegative group projector

In this paper, the most usual matrix partial orders are considered on the ring of real matrices. These orders are studied on at most index 1 matrices having nonnegative group projector by using a specific block structure. The goal of this paper is to analyze how this structure is inherited by predecessors ordered under minus, sharp, star, and one-sided orders. In addition, the case of arbitrary index (greater than 1) is also investigated by means of the cn-partial order and using the Drazin inverse.