Numerical ranges of companion matrices

Hwa Long Gau, Pei Yuan Wu

研究成果: 雜誌貢獻期刊論文同行評審

8 引文 斯高帕斯(Scopus)

摘要

We show that an n-by-n companion matrix A can have at most n line segments on the boundary ∂W(A) of its numerical range W(A), and it has exactly n line segments on ∂W(A) if and only if, for n odd, A is unitary, and, for n even, A is unitarily equivalent to the direct sum A1 ⊕ A2 of two (n/2)-by-(n/2) companion matricesA1 = fenced((0, 1; 0, {triple dot, diagonal NW-SE}; {triple dot, diagonal NW-SE}, 1; a, 0)) and A2 = fenced((0, 1; 0, {triple dot, diagonal NW-SE}; {triple dot, diagonal NW-SE}, 1; - 1 / over(a, ̄), 0)) with 1 ≤ {divides}a{divides} < tan(π/n) + sec(π/n).

原文???core.languages.en_GB???
頁(從 - 到)202-218
頁數17
期刊Linear Algebra and Its Applications
421
發行號2-3 SPEC. ISS.
DOIs
出版狀態已出版 - 1 3月 2007

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