Farkas' lemma and multilinear forms
type: Item
instance of: scholarly article
title: Farkas' lemma and multilinear forms
zbMATH Open document ID: 1176.46004
author: Larry Downey
published in: Missouri Journal of Mathematical Sciences
publication date: 2009-04-14T00:00:00Z
review text: The author shows that the analogue of Farkas' Lemma can fail if one substitutes linear forms with bilinear ones. Specifically, he provides an example of three bilinear forms \(A, B,\) and \(C\) taking \(\mathbb R^2 \times \mathbb R^2 \to \mathbb R\) with the following property: Whenever \(A(x,y) \geq 0\) and \(B(x,y) \geq 0,\) then \(C(x,y) \geq 0,\) although \(C\) is not a linear combination of \(A\) and \(B.\) Further details and a related positive result are available in work by \textit{M.\,Maestre}, the author, and the reviewer [Note Mat.\ 25(2005--2006), No.\,1, 49--54 (2006; Zbl 1221.15034)].
Mathematics Subject Classification ID: 46A22
Mathematics Subject Classification ID: 47A07
Mathematics Subject Classification ID: 15A69
zbMATH DE Number: 5542878
zbMATH Keywords: bilinear forms
zbMATH Keywords: Farkas lemma
reviewed by: Richard M. Aron
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5542878