Numerical ranges of companion matrices: flat portions on the boundary

Details Numerical ranges of companion matrices: flat portions on the boundary Numerical ranges of companion matrices: flat portions on the boundary

2011-07-15

arxiv.org/abs/1107.3070v1

Mathematics

Functional Analysis

18 pages, 4 figures

Scientific paper

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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