TY - JOUR T1 - Linear Functions Preserving Multivariate and Directional Majorization TT - JF - IJMSI JO - IJMSI VL - 5 IS - 1 UR - http://ijmsi.ir/article-1-105-en.html Y1 - 2010 SP - 1 EP - 5 KW - Doubly Stochastic matrices KW - Directional majorization KW - Multivariate majorization KW - Linear preserver. N2 - Let V and W be two real vector spaces and let &sim be a relation on both V and W. A linear function T : V → W is said to be a linear preserver (respectively strong linear preserver) of &sim if Tx &sim Ty whenever x &sim y (respectively Tx &sim Ty if and only if x &sim y). In this paper we characterize all linear functions T : M_{n,m} → M_{n,k} which preserve or strongly preserve multivariate and directional majorization. M3 10.7508/ijmsi.2010.01.001 ER -