Mathematical Inequalities & Applications · Volume 7, Issue 3 A variational proof of Birkhoff's theorem on doubly stochastic matrices 07-34 Pages 309-313 DOI 10.7153/mia-07-34 Downloads Short PDF Full PDF PNG Authors Qiji J. Zhu Keywords variational method doubly stochastic matrix majorization Birkhoff theorem Subject classes 15A42 15A51 58E30