Hyperbolic forms associated with cyclic weighted shift matrices

被引：9

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 | 2013年 / 439卷 / 11期

关键词：

Hyperbolic form; Cyclic weighted shift matrix; Reducibility; Numerical range; RANK NUMERICAL RANGES; POLYNOMIALS; OPERATORS; RADIUS;

D O I：

10.1016/j.laa.2013.09.018

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The singular points of the curve of a hyperbolic form associated with a cyclic weighted shift matrix are examined. It is shown that the singular points of such a curve are real nodes. Some results related the numerical ranges of cyclic weighted shift matrices are presented. In particular, the existence of flat portions on the boundary of the numerical range depends on the reducibility of the hyperbolic form. Further, an algebraic method is provided for the decomposition of reducible form which leads to a criterion for the periodicity of the weights. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：3541 / 3554

页数：14

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