Elliptic numerical ranges of 3x3 companion matrices

被引：7
|
作者：
Calbeck, William [1 ]
机构：
[1] Louisiana State Univ, Dept Math & Phys Sci, Alexandria, LA 71302 USA
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2008年 / 428卷 / 11-12期
关键词：
companion matrix; numerical range;
D O I：
10.1016/j.laa.2007.12.018
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A companion matrix is determined by the zeros of its characteristic polynomial. We determine the location of the zeros which yields an elliptic numerical range. In particular we show that given any two complex numbers z(1) and z(2) there exists a third complex number z(3) such that the companion matrix of the polynomial (z-z(1)) (z-z(2)) (z-z(3)) will have elliptic numerical range with foci at z(1) and z(2). (C) 2008 Elsevier Inc. All rights reserved.
引用
收藏
页码：2715 / 2722
页数：8
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