The Birkhoff theorem for unitary matrices of arbitrary dimensions

S. De Baerdemacker, A. De Vos (Alexis), L. Chen, L. Yu
Linear Algebra and its Applications
514,151–164
2016
A1

Abstract 

It was shown recently that Birkho's theorem for doubly stochastic matrices
can be extended to unitary matrices with equal line sums whenever the dimension
of the matrices is prime. We prove a generalization of the Birkho
theorem for unitary matrices with equal line sums for arbitrary dimension.