Numerical ranges of companion matrices: flat portions on the boundary

Autor:	Eldred, Jeffrey, Rodman, Leiba, Spitkovsky, Ilya M.
Rok vydání:	2011
Předmět:	Mathematics - Functional Analysis Mathematics - Algebraic Geometry 15
Druh dokumentu:	Working Paper
Popis:	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. Comment: 18 pages, 4 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1107.3070 Zobrazit plný text záznamu View this record from Arxiv