THE STRUCTURE OF STRONG LINEAR PRESERVERS OF GW-MAJORIZATION ON Mn,m

Let Mn,m be the set of all n*m real matrices. Matrix RЄMn with the property Re=e, is said to be a g-row stochastic (generalized row stochastic) matrix. Let A,B Є Mn,m, so B is said to be gw-majorized by A if there exists an n*n g-row stochastic matrix R such that B=RA. In this paper we characterize all linear operators that strongly preserve gw-majorization on Mn,m and all linear operators that strongly preserve matrix majorization on Mn.

Keywords:

Preserver , strong preserver , g-row stochastic matrices , gw-mahorization