A mapping from the unitary to doubly stochastic matrices and symbols on a finite set
arXiv:0806.2357 · doi:10.1063/1.3043870
Abstract
We prove that the mapping from the unitary to the doubly stochastic matrices that maps a unitary matrix (u_{kl}) to the doubly stochastic matrix (|u_{kl}|^2) is a submersion for almost all unitary matrices. The proof uses the framework of operator symbols on a finite set. We give detailed proofs of the results announced in our earlier preprint.
13 pages