Higher-rank numerical ranges and Kippenhahn polynomials

Please use this identifier to cite or link to this item: https://ir.lib.ncu.edu.tw/handle/987654321/109226

Title:	Higher-rank numerical ranges and Kippenhahn polynomials
Authors:	高華隆;Gau, Hwa-Long;Wu, Pei Yuan
Contributors:	理學院數學系
Keywords:	15A60;Higher-rank numerical range;Kippenhahn polynomial
Date:	2013-04-01
Issue Date:	2026-04-23 16:16:38 (UTC+8)
Publisher:	Elsevier Inc.;Elsevier Inc
Abstract:	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. 出版者： Elsevier Inc 出版日期： 2013-04-01 出處： Linear Algebra and its Applications, 2013-04, Vol.438 (7), p.3054-3061 資源來源： Elsevier ScienceDirect Journals Complete 版權： 2012 Elsevier Inc. 識別號： ISSN: 0024-3795 識別號： EISSN: 1873-1856 識別號： DOI: 10.1016/j.laa.2012.11.017
Appears in Collections:	[Department of Mathematics] journal & Dissertation

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