Numerical ranges of reducible companion matrices

研究成果: 雜誌貢獻期刊論文同行評審

7 引文 斯高帕斯(Scopus)

摘要

In this paper, we show that a reducible companion matrix is completely determined by its numerical range, that is, if two reducible companion matrices have the same numerical range, then they must equal to each other. We also obtain a criterion for a reducible companion matrix to have an elliptic numerical range, put more precisely, we show that the numerical range of an n-by-n reducible companion matrix C is an elliptic disc if and only if C is unitarily equivalent to A ⊕ B, where A ∈ Mn - 2, B ∈ M2 with σ (B) = {a ω1, a ω2}, ω1n = ω2n = 1, ω1 ≠ ω2, and | a | ≥ fenced(| ω1 + ω2 | + sqrt(| ω1 + ω2 |2 + 4 (1 + 2 cos (π / n)))) / 2.

原文???core.languages.en_GB???
頁(從 - 到)1310-1321
頁數12
期刊Linear Algebra and Its Applications
432
發行號5
DOIs
出版狀態已出版 - 15 2月 2010

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