On flat portions on the boundary of the numerical range

被引：29
作者：
Brown, ES
Spitkovsky, IA [1 ]
机构：
[1] Coll William & Mary, Dept Math, Williamsburg, VA 23187 USA
[2] MIT, Dept Math, Cambridge, MA 02139 USA
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2004年 / 390卷
基金：
美国国家科学基金会;
关键词：
numerical range; tridiagonal matrices; unitary (ir)reducibility;
D O I：
10.1016/j.laa.2004.04.009
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The paper is devoted to matrices with flat portions on the boundary of their numerical range. A constructive criterion for such portions to exist is obtained in case of tridiagonal matrices, and a particular case of continuant matrices is considered. As an application, the cases of (arbitrary) 3 x 3 and 4 x 4 matrices are treated. It is shown, in particular, that the sharp bound for the number of flat portions on the boundary of the numerical range for 4 x 4 matrices is four (three, if the matrices are assumed unitarily irreducible). (C) 2004 Elsevier Inc. All rights reserved.
引用
收藏
页码：75 / 109
页数：35
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