The boundary of higher rank numerical ranges

被引：14

作者：

Chien, Mao-Ting ^{[1
]}

Nakazato, Hiroshi ^{[2
]}

机构：

[1] Soochow Univ, Dept Math, Taipei 11102, Taiwan

[2] Hirosaki Univ, Fac Sci & Technol, Dept Math Sci, Hirosaki, Aomori 0368561, Japan

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2011年 / 435卷 / 11期

关键词：

Rank-k-numerical range; Flat portion; Singular point; Roulette curve;

D O I：

10.1016/j.laa.2011.05.020

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The rank-k-numerical range of an n x n matrix A is defined as Lambda(k) (A) = {lambda is an element of C : PAP = lambda P for some rank k orthogonal projection P}. This study presents a method to generate the boundary of Lambda(k)(A), and examines the flat portions of the boundary of the rank-k-numerical range of a matrix associated with a roulette curve. A sufficient condition is given to ensure that the rank-k-numerical range is not attainable by a classical numerical range. (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：2971 / 2985

页数：15

共 15 条

[1] Construction of determinantal representation of trigonometric polynomials [J].