Unimodular systems of vectors are embeddable in the \((0, 1)\)-cube
type: Item
instance of: scholarly article
title: Unimodular systems of vectors are embeddable in the \((0, 1)\)-cube
zbMATH Open document ID: 1236.15001
DOI: 10.1134/S0001434610110301
author: G. A. Koshevoy
author: Viacheslav Grishukhin
author: Vladimir I. Danilov
published in: Mathematical Notes
publication date: 2011-11-25T00:00:00Z
review text: Let \(U^+\cup U^-\) be a partition of an \(n\)-dimensional unimodular system \(U\) whose vectors span \(\mathbb{R}^n\). The authors prove that the vectors of \(U^\prime=U^+\cup \{-u\, : \, u\in U^-\}\) have \((0,1)\)-coordinates in the dual basis of a particular set of linearly independent edges of the polyhedron \(P=\{ x\in\mathbb{R}^n : 0\leqslant u^Tx\leqslant 1 \text{ for any }u\in U^\prime\)
Mathematics Subject Classification ID: 15A03
Mathematics Subject Classification ID: 52A05
zbMATH DE Number: 5980734
zbMATH Keywords: unimodular system of vectors
zbMATH Keywords: \((0,1)\)-cube
zbMATH Keywords: basis
zbMATH Keywords: linearly independent edges
zbMATH Keywords: polyhedron
reviewed by: C. M.da Fonseca
MaRDI profile type: Publication
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full work available at URL: s0001434610110301
OpenAlex ID: W1966635326
description: scientific article; zbMATH DE number 5980734