Companion matrices: Reducibility, numerical ranges and similarity to contractions

Hwa Long Gau, Pei Yuan Wu

研究成果: 雜誌貢獻期刊論文同行評審

25 引文 斯高帕斯(Scopus)

摘要

In this paper, we study some unitary-equivalence properties of the companion matrices. We obtain a criterion for a companion matrix to be reducible and show that the numerical range of a companion matrix is a circular disc centered at the origin if and only if the matrix equals the (nilpotent) Jordan block. However, the more general assertion that a companion matrix is determined by its numerical range turns out to be false. We also determine, for an n×n matrix A with eigenvalues in the open unit disc, the defect index of a contraction to which A is similar.

原文???core.languages.en_GB???
頁(從 - 到)127-142
頁數16
期刊Linear Algebra and Its Applications
383
發行號1-3 SPEC. ISS.
DOIs
出版狀態已出版 - 15 5月 2004

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