Birkhoff polytope

The Birkhoff polytope B_n (also called the assignment polytope, the polytope of doubly stochastic matrices, or the perfect matching polytope of the complete bipartite graph ${\displaystyle K_{n,n}}$^[1]) is the convex polytope in R^N (where N = n²) whose points are the doubly stochastic matrices, i.e., the n × n matrices whose entries are non-negative real numbers and whose rows and columns each add up to 1. It is named after Garrett Birkhoff.