Linear operators preserving multivariate majorization (Q1970498)

Let \(A\) and \(B\) be \(m\times n\) real matrices. Then \(A\) is multivariate majorized by \(B\), \(A\prec B\), if \(A=BD\) for some doubly stochastic \(n\times n\) matrix \(D\). The author gives a complete characterization of all linear transformations \(T\) of the space of \(m\times n\) real matrices that preserve multivariate majorization: if \(A\prec B\), then \(T(A)\prec T(B)\).