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arXiv · 1107.3070

Numerical ranges of companion matrices: flat portions on the boundary

Jeffrey Eldred·Leiba Rodman·Ilya M. Spitkovsky
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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-by-3 and 4-by-4 matrices. In the latter case, it is proved that a 4-by-4 unitarily irreducible companion matrix cannot have 3 flat portions on the boundary of its numerical range. Numerical examples are given to illustrate the main results.

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Jeffrey Eldred, Leiba Rodman, Ilya M. Spitkovsky. 2011-07-15. Numerical ranges of companion matrices: flat portions on the boundary. https://arxiv.org/abs/1107.3070

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