Permanents of special classes of doubly stochastic matrices
Paul J. Knopp, Richard Sinkhorn · Linear and Multilinear Algebra · 1976
We identify the doubly stochastic matrices with at least one zero entry which are closest in the Euclidean norm to Jn , the matrix with each entry equal to 1/n, and we show that at these matrices the permanent function has a relative minimum when restricted to doubly stochastic matrices having zero entries.