Numerical ranges of companion matrices: flat portions on the boundary

Jeffrey Eldred; Leiba Rodman; Ilya Spitkovsky

doi:10.1080/03081087.2011.634415

Numerical ranges of companion matrices: flat portions on the boundary

Jeffrey Eldred, Leiba Rodman, Ilya Spitkovsky

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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 × 3 and 4 × 4 matrices. In the latter case, it is proved that a 4 × 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.

Original language	English (US)
Pages (from-to)	1295-1311
Number of pages	17
Journal	Linear and Multilinear Algebra
Volume	60
Issue number	11-12
DOIs	https://doi.org/10.1080/03081087.2011.634415
State	Published - Nov 2012

Keywords

companion matrix
numerical range

ASJC Scopus subject areas

Algebra and Number Theory

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10.1080/03081087.2011.634415

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Numerical ranges of companion matrices: flat portions on the boundary

Abstract

Keywords

ASJC Scopus subject areas

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