Strict convexity of the joint \(c\)-numerical range
type: Item
instance of: scholarly article
title: Strict convexity of the joint \(c\)-numerical range
zbMATH Open document ID: 1270.15013
author: Mao-Ting Chien
author: Hiroshi Nakazato
published in: Linear Algebra and its Applications
publication date: 2013-01-16T00:00:00Z
review text: Let \(H_{n}\) be the real vector space of \(n\times n\) complex Hermitian matrices. For any \(c=(c_{1},c_{2},\dots,c_{n})\in \mathbb R^{n}\) and an ordered \(m\)-tuple \(H=(H_{1},H_{2},\dots,H_{m})\in H_{n}^{m}\), the joint \(c\)-numerical range \(W_{c}(H)\) of \(H\) is defined. This paper investigates the outer boundary curve of the joint \(c\)-numerical range \(W_{c}(H_{1},H_{2},\dots,H_{m}) \), presents a sufficient condition for the outer boundary of the joint \(c\)-numerical range to contain no line segments, and discusses the strict convexity of the convex hull of the joint \(c\)-numerical range.
Mathematics Subject Classification ID: 15A60
Mathematics Subject Classification ID: 52A30
zbMATH DE Number: 6125866
zbMATH Keywords: joint \(c\)-numerical range
zbMATH Keywords: strictly convex set
zbMATH Keywords: weakly strictly hyperbolic form
zbMATH Keywords: convex hull
MaRDI profile type: Publication
full work available at URL: j.laa.2012.09.004
OpenAlex ID: W1964826751
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DOI: 10.1016/J.LAA.2012.09.004
description: scientific article; zbMATH DE number 6125866