Let $x$ a vector in $d$ dimensions with positive entries summing to one (a probability distribution). Is there a characterization of the linear operators $T:R^{d}_{+}\to R^{d}_{+}$ such that: $$ x\prec Tx $$ for all probability distributions $x$, with $\prec$ the majorization order? Thanks Fabio
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$\begingroup$ Could you please specify what you mean by "majorization order"? $\endgroup$– Jochen GlueckCommented Oct 15, 2019 at 15:54
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$\begingroup$ Is an order on vectors, see e.g. en.wikipedia.org/wiki/Majorization $\endgroup$– FabioCommented Oct 16, 2019 at 6:35
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