Geodesic
Linear preservers of left matrix majorization
The electronic journal of linear algebra, Tome 17 (2008), pp. 304-315.

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

Summary: For X, Y $\in M$ nm ( R) (= M nm ), we say that Y is left (resp. right) matrix majorized by X and write Y $\prec X$ (resp. Y $\prec r$ X) if Y = RX (resp. Y = XR) for some row stochastic matrix R. A linear operator T : M nm $\rightarrow M$ nm is said to be a linear preserver of a given relation $\prec $on M nm if Y $\prec X$ implies that T Y $\prec T$ X. The linear preservers of $\prec $or $\prec r$ are fully characterized by A.M.
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 = {Linear preservers of left matrix majorization},
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Khalooei, Fatemeh; Radjabalipour, Mehdi; Torabian, Parisa. Linear preservers of left matrix majorization. The electronic journal of linear algebra, Tome 17 (2008), pp. 304-315. http://geodesic.mathdoc.fr/item/ELA_2008__17__a23/