Right gw-Majorization on M_{n,m}

Let Mn,m be the set of all n×m matrices with entries in F, where F is the field of real or complex numbers. A real or complex n×n matrix is generalized row stochastic (g-row stochastic) if all of its row sums equal one. For X, Y 2 Mn,m , we say that Y is right gw-majorized by X and write X rgw Y if Y=XR for some g-row stochastic matrix R. Here, we characterize all strong linear preservers of rgw on Mn,m.