Positive linear functionals and the order cone
type: Item
instance of: scholarly article
title: Positive linear functionals and the order cone
zbMATH Open document ID: 0679.15015
DOI: 10.1016/0024-3795(89)90573-9
author: Peter Volkmann
author: Ray Redheffer
published in: Linear Algebra and its Applications
publication date: 1989-01-01T00:00:00Z
review text: Let P be the cone of \(n\times n\) complex matrices with positive semi- definite Hermitean part and let \(P^*\) be the dual cone. The paper shows equality of two expressions defined for \(p\in \partial P\) and q arbitrary, namely max Re(cq) over all \(c\in P^*\) satisfying \(cI=1\) and \(Re(cp)=0\) equals max Re(\(\xi\),q\(\xi)\) over all vectors \(\xi\) of norm one satisfying \((p+p^*)\xi =0\).
Mathematics Subject Classification ID: 15A30
Mathematics Subject Classification ID: 15A60
Mathematics Subject Classification ID: 47L07
zbMATH DE Number: 4112782
zbMATH Keywords: cone of complex matrices
zbMATH Keywords: positive linear functionals
zbMATH Keywords: order cone
zbMATH Keywords: dual cone
reviewed by: Tage Bai Andersen
MaRDI profile type: Publication
full work available at URL: 0024-3795(89)90573-9
OpenAlex ID: W1990642642
cites work: Differential equations in operator algebras. II: Invariance of the order cone
cites work: A Characterization of Positive Linear Functionals and Oscillation Criteria for Matrix Differential Equations
description: scientific article; zbMATH DE number 4112782