Some characterizations of the left-star, right-star, and star partial orderings between matrices of the same size are obtained. Based on those results, several characterizations of the star partial ordering between EP matrices are given. At last, one characterization of the sharp partial ordering between group matrices is obtained.
"Some Results on Characterizations of Matrix Partial Orderings." J. Appl. Math. 2014 (SI04) 1 - 6, 2014. https://doi.org/10.1155/2014/408457