Higher-rank numerical ranges and Kippenhahn polynomials

Hwa Long Gau, Pei Yuan Wu

研究成果: 雜誌貢獻期刊論文同行評審

9 引文 斯高帕斯(Scopus)

摘要

We prove that two n-by-n matrices A and B have their rank-k numerical ranges Λk(A) and Λk(B) equal to each other for all k,1≤k≤⌊n/2⌋+1, if and only if their Kippenhahn polynomials pA(x,y,z)≡det(xReA+yImA+zIn) and pB(x,y,z)≡det(xReB+yImB+zIn) coincide. The main tools for the proof are the Li-Sze characterization of higher-rank numerical ranges, Weyl's perturbation theorem for eigenvalues of Hermitian matrices and Bézout's theorem for the number of common zeros for two homogeneous polynomials.

原文???core.languages.en_GB???
頁(從 - 到)3054-3061
頁數8
期刊Linear Algebra and Its Applications
438
發行號7
DOIs
出版狀態已出版 - 1 4月 2013

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