# Linear maps that increase majorization order

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