A geometric Gordan-Stiemke theorem
type: Item
instance of: scholarly article
title: A geometric Gordan-Stiemke theorem
zbMATH Open document ID: 0547.15008
DOI: 10.1016/0024-3795(84)90023-5
author: Norbil Davila
author: George Phillip Barker
author: Bit-Shun Tam
published in: Linear Algebra and its Applications
publication date: 1984-01-01T00:00:00Z
review text: Let C and K be closed cones in \(R^ n\). Denote by \(\phi\) (\(K\cap C)\) the face of C generated by \(K\cap C\), and by \(\phi (-K^*\cap C^*)\) the face of \(C^*\) generated by \(-K^*\cap C^*\). Then \((i)\quad\phi (K\cap C)\subseteq\phi (-K^*\cap C^*)^ D,\) where the equality holds iff \(C\cap [span(-K^*\cap C^*)]^{\perp}\subseteq K-C;\) and \((ii)\quad\phi (-K^*\cap C^*)\subseteq\phi (K\cap C)^ D,\) where the equality holds iff \(-C^*\cap [span(K\cap C)]^{\perp}\subseteq C^*+K^*.\) Hence a generalization of the Gordan-Stiemke theorem follows.
Mathematics Subject Classification ID: 15A39
Mathematics Subject Classification ID: 06F20
zbMATH DE Number: 3871563
zbMATH Keywords: partially ordered spaces
zbMATH Keywords: closed cones
zbMATH Keywords: Gordan-Stiemke theorem
reviewed by: Sándor Lajos
MaRDI profile type: Publication
full work available at URL: 0024-3795(84)90023-5
OpenAlex ID: W2060489438
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description: scientific article; zbMATH DE number 3871563