Boundary generating curves of the \(c\)-numerical range
type: Item
instance of: scholarly article
title: Boundary generating curves of the \(c\)-numerical range
zbMATH Open document ID: 0932.15017
DOI: 10.1016/S0024-3795(99)00055-5
author: Mao-Ting Chien
author: Hiroshi Nakazato
published in: Linear Algebra and its Applications
publication date: 1999-11-29T00:00:00Z
review text: Let \(A\) be an \(n\)-by-\(n\) matrix and \(c=(c_1,\dots,c_n)\) be a real \(n\)-tuple. The \(c\)-numerical range of~\(A\) is the set \(W_c=\{\sum^n_{j=1}c_jx^*_jAx_j\mid \{x_1,\dots,x_n\}\) is an orthogonal basis of~\({\mathbb C}^n\}\). The authors obtain parametric representations of the boundary generating curve of the \(c\)-numerical range of a matrix and give a description of the boundary generating curves of the \(c\)-numerical range of certain types of nilpotent Toeplitz matrices. A sufficient condition for the boundary generating curve to be rational is obtained. Finally, the authors compute the boundary generating curves of the numerical ranges for several concrete matrices and classify the rationality of the curves.
Mathematics Subject Classification ID: 15A60
Mathematics Subject Classification ID: 15B57
Mathematics Subject Classification ID: 14G05
zbMATH DE Number: 1371392
zbMATH Keywords: \(c\)-numerical range
zbMATH Keywords: boundary generating curve
zbMATH Keywords: generalized circulant matrix
zbMATH Keywords: rational curve
zbMATH Keywords: genus
zbMATH Keywords: nilpotent Toeplitz matrices
reviewed by: A. R. Alimov
MaRDI profile type: Publication
full work available at URL: s0024-3795(99)00055-5
OpenAlex ID: W2001674675
description: scientific article; zbMATH DE number 1371392