A Note on Gordan's Theorem
Cherng-Tiao Perng *
Department of Mathematics, Norfolk State University, 700 Park Avenue, Norfolk, Virginia 23504, USA.
*Author to whom correspondence should be addressed.
Abstract
Inspired by Gale's proof of Farkas's lemma, this expository note aims to give a very simple and intuitive proof of Gordan's theorem and the equivalence of this theorem to Farkas's lemma and some formulations of the separating hyperplane theorems. The tool we have employed is limited to only very simple linear algebra over the eld of real numbers.
Keywords: Gordan's theorem, Farkas's lemma, separating hyperplane theorem, Stiemke's theorem