Volume 7, Issue 3 Qiji J. Zhu A variational proof of Birkhoff's theorem on doubly stochastic matrices Downloads Abstract PDF Full article PDF DOI { copied = true; setTimeout(() => copied = false, 2000) })" :aria-label="copied ? 'DOI copied' : 'Copy DOI'" :title="copied ? 'Copied' : 'Copy DOI'" > Find all available articles from these authors Qiji J. Zhu Find more articles with the same keywords variational method doubly stochastic matrix majorization Birkhoff theorem Find more articles with the same subject classes 15A42 15A51 58E30