LINEAR FUNCTIONS PRESERVING UPPER TRIANGULAR MAJORIZATION ON R2

Let Mn be the algebra of all n £ n real matrices. A matrix R 2 Mn with nonnegative entries is called row stochastic if Re = e, where e = (1; : : : ; 1)t 2 Rn. For x; y 2 Rn, we say that x is upper triangular majorized by y (write as x Áut y ) if there exists an upper triangular row stochastic matrix R such that x = Ry. In this paper, after introducing the relation Áut, the geometric interpretation of Áut on Rn is obtained and also the structure of all linear functions T : R2 ! R2, preserving (or strongly preserving) Áut are characterized.