Numerical ranges of companion matrices: flat portions on the boundary

被引：6

作者：

Eldred, Jeffrey ^{[2
]}

Rodman, Leiba ^{[1
]}

Spitkovsky, Ilya ^{[1
]}

机构：

[1] Coll William & Mary, Dept Math, Williamsburg, VA 23185 USA

[2] Indiana Univ, Dept Phys, Bloomington, IN 47408 USA

来源：

LINEAR & MULTILINEAR ALGEBRA | 2012年 / 60卷 / 11-12期

关键词：

numerical range; companion matrix;

D O I：

10.1080/03081087.2011.634415

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Criterion for a companion matrix to have a certain number of flat portions on the boundary of its numerical range is given. The criterion is specialized to the cases of 3 x 3 and 4 x 4 matrices. In the latter case, it is proved that a 4 x 4 unitarily irreducible companion matrix cannot have three flat portions on the boundary of its numerical range. Numerical examples are given to illustrate the main results.

引用

页码：1295 / 1311

页数：17

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