On geometric properties of the numerical range

被引：20

作者：

Chien, MT ^{[1
]}

Yeh, L

Yeh, YT

Lin, FZ

机构：

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

[2] Lih Chih Sch Technol & Commerce, Kaohsiung 80708, Taiwan

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 1998年 / 274卷

关键词：

D O I：

10.1016/S0024-3795(97)00373-X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate the shape of the numerical range. A criterion for the numerical range of a matrix to be an elliptical disk is given. The result is applied to show that there exist neither 3-by-3 nor 4-by-4 nilpotent matrices whose numerical range is an elliptical (noncircular) disk. Sufficient conditions for n-by-n tridiagonal matrices to have elliptical numerical range are obtained. The boundary of the numerical range near a sharp point is examined. Finally, the numerical range of a reducible matrix is compressed, and its geometric properties are discussed. (C) 1998 Elsevier Science Inc.

引用

页码：389 / 410

页数：22

共 11 条

[1]

[Anonymous], LINEAR MULTILINEAR A

[2] NUMERICAL RANGE OF A MATRIX - SOME EFFECTIVE CRITERIA [J].