In this paper, we mainly introduce some equivalent conditions for SEP matrices. Firstly, we provide characterizations of SEP matrices in terms of projections. Secondly, we characterize SEP matrices by the representations of group inverses and Moore-Penrose inverses. Finally, we propose characterizations of SEP matrices, specifically by constructing three matrix equations and discussing whether they have solutions in given sets to determine whether a group invertible matrix is a SEP matrix respectively.
Liu et al. (Wed,) studied this question.