Sinkhorn limits in finitely many steps (1912.00095v2)

Abstract: Applied to a nonnegative $m\times n$ matrix with a nonzero $\sigma$-diagonal, the sequence of matrices constructed by alternate row and column scaling conveges to a doubly stochastic matrix. It is proved that if this sequence converges after only a finite number of scalings, then it converges after at most two scalings.