Right gut-majorization on M_{n,m}

Let M_{n,m} be the set of all n-by-m matrices with entries from R, and suppose that R^n is the set of all 1-by-n real row vectors. A matrix R is called generalized row stochastic (g-row stochastic) if the sum of entries on every row of R is 1. For X, Y ? M_{n,m}, it is said that X is rgut-majorized by Y (denoted by X ?_{rgut} Y ) if there exists an m-by-m upper triangular g-row stochastic matrix R such that X = Y R. In this paper, the concept right upper triangular generalized row stochastic majorization, or rgut- majorization, is investigated and then the linear preservers and strong linear preservers of this concept are characterized on R^n and M_{n,m}.