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
收藏
页码：1295 / 1311
页数：17
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