Vector majorization via positive definite matrices Original Research Article

It is well known that for real n-vectors y and x, y majorizes x if and only if Ay = x for some doubly stochastic matrix A of order n. If the components of each of y and x are in nonincreasing order, then it is known that the matrix A can be chosen to be positive semidefinite symmetric. We characterize when there is a positive definite doubly stochastic matrix A such that Ay = x.