  Let M_{n,m} be the set of all n by m matrices with entries in F, where F is
the field of real or complex numbers. A matrix R in M_{n} with the property
Re=e, is said to be a g-row stochastic (generalized row stochastic) matrix. Let
A,B in M_{n,m}, so B is said to be gw-majorized by A if there exists an n by n
g-row stochastic matrix R such that B=RA. In this paper we characterize all
linear operators that strongly preserve gw-majorization on M_{n,m} and all
linear operators that strongly preserve matrix majorization on M_{n} .
