Some Results on Majorization of Matrices

For two n×m real matrices X and Y, is said to be majorized by written as X≺Y if X=SY for some doubly stochastic matrix of order n. Matrix majorization has several applications in statistics, wireless communications other fields science engineering. Hwang Park obtained the necessary sufficient conditions X,Y satisfy cases where rank Y=n−1 Y=n. In this paper, we obtain Y=n−2 general Y=n−k, 1≤k≤n−1. We Y with on Y. The there S∈Ωm such that X=YS. introduced a new concept column paper. A denoted X⪯cY, exists S X=SY. give characterizations (0,1) matrices.