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
