Geodesic
The structure of linear preservers of left matrix majorization on $\Bbb R^p$
The electronic journal of linear algebra, Tome 18 (2009), pp. 88-97.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: For vectors X, Y $\in R$ n , Y is said to be left matrix majorized by X (Y $\prec X$) if for some row stochastic matrix R, Y = RX. A linear operator T : R p $\rightarrow R$ n is said to be a linear preserver of $\prec $if Y $\prec X$ on R p implies that T Y $\prec T$ X on R n . The linear operators T : R p $\rightarrow R$ n ( n p$(p - 1))$ which preserve $\prec $have been characterized. In this paper, linear operators T : R p $\rightarrow R$ n which preserve $\prec $are characterized without any condition on n and p.
Classification : 15A04, 15A21, 15A51
Keywords: row stochastic matrix, doubly stochastic matrix, matrix majorization, weak matrix majorization, left (right) multivariate majorization, linear preserver 
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     title = {The structure of linear preservers of left matrix majorization on $\Bbb R^p$},
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Khalooei, Fatemeh; Salemi, Abbas. The structure of linear preservers of left matrix majorization on $\Bbb R^p$. The electronic journal of linear algebra, Tome 18 (2009), pp. 88-97. http://geodesic.mathdoc.fr/item/ELA_2009__18__a50/