A note on multivariate majorization

‎A matrix A is said to be multivariate majorized by a matrix B‎, ‎written A\prec B‎, ‎if there exists a doubly stochastic matrix D such that A = BD‎ . ‎In the present paper‎, ‎we obtain a totally ordered subset of M_{nm} which contains a given matrix A‎. ‎Also‎, ‎we show that the totality of all extreme points of the collection of all the matrices which are multivariate‎ly‎ majorized by a matrix A is the set of all matrices obtained by permuting the columns of A‎.

کلیدواژه ها:

doubly stochastic‎ ، ‎extreme point ، ‎multivariate majorization