RT - Journal Article T1 - Linear Functions Preserving Multivariate and Directional Majorization JF - IJMSI YR - 2010 JO - IJMSI VO - 5 IS - 1 UR - http://ijmsi.ir/article-1-105-en.html SP - 1 EP - 5 K1 - Doubly Stochastic matrices K1 - Directional majorization K1 - Multivariate majorization K1 - Linear preserver. AB - 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. LA eng UL http://ijmsi.ir/article-1-105-en.html M3 10.7508/ijmsi.2010.01.001 ER -