Row and column-majorization on Mn,m

Let Mn,m be the set of all n×m matrices with entries in R. For A,B∈Mn,m, it is said that A is row majorized (respectively column-majorized) by B if every row (respectively column) of A is majorized by the corresponding row (respectively column) of B, i.e. for every i () there exists a doubly stochastic matrix Di such that A(i)=B(i)Di, where A(i) and B(i) are the ith rows of A and B respectively. In this paper the relations row and column-majorization on Mn,m are studied and also all linear operators T:Mn,m→Mn,m preserving (or strongly preserving) row or column-majorization will be characterized.