Condition for the numerical range to contain an elliptic disc

DOI10.1016/S0024-3795(02)00548-7zbMath1026.15018OpenAlexW1975914076MaRDI QIDQ1870073

Pei Yuan Wu, Hwa-Long Gau

Publication date: 4 May 2003

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0024-3795(02)00548-7

zbMATH Keywords

numerical rangePoncelet propertyKippen-Hahn curve

Mathematics Subject Classification ID

Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60)

Related Items (29)

Extremality of numerical radii of matrix products ⋮ Convexity of the Berezin range ⋮ Ellipses and compositions of finite Blaschke products ⋮ Numerical radii for tensor products of matrices ⋮ Elementary proofs for some results on the circular symmetry of the numerical range ⋮ Numerical ranges of reducible companion matrices ⋮ On the boundary of rank-knumerical ranges ⋮ Poncelet's porism in the finite real plane ⋮ Extremality of numerical radii of matrix commutators and Jordan products ⋮ Poncelet-Darboux, Kippenhahn, and Szegő: interactions between projective geometry, matrices and orthogonal polynomials ⋮ Numerical ranges and Geršgorin discs ⋮ Factorization of Singular Matrix Polynomials and Matrices with Circular Higher Rank Numerical Ranges ⋮ On numerical ranges of the compressions of normal matrices ⋮ Decomposable Blaschke products of degree 2ⁿ ⋮ Numerical range of Lie product of operators ⋮ A note on Anderson's theorem in the infinite-dimensional setting ⋮ Structures and numerical ranges of power partial isometries ⋮ Numerical ranges as circular discs ⋮ Numerical ranges of weighted shift matrices with periodic weights ⋮ Decomposing finite Blaschke products ⋮ Circular numerical ranges of partial isometries ⋮ On the boundary of weighted numerical ranges ⋮ Möbius transformations and Blaschke products: the geometric connection ⋮ Curves of geodesic centers and Poncelet ellipses ⋮ Equality of numerical ranges of matrix powers ⋮ Anderson’s theorem for compact operators ⋮ A characterization of complex plane Poncelet curves ⋮ Anderson's theorem and \(A\)-spectral radius bounds for semi-Hilbertian space operators ⋮ Noncircular elliptic discs as numerical ranges of nilpotent operators

Cites Work

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• The upper numerical range of a quaternionic matrix is not a complex numerical range
• Geometry of the numerical range of matrices
• On the geometry of numerical ranges
• Perron-Frobenius type results on the numerical range
• Numerical ranges and Poncelet curves
• On matrices whose numerical ranges have circular or weak circular symmetry
• Numerical range ofs(φ)
• Model theory and linear extreme points in the numerical radius unit ball
• Über den Wertevorrat einer Matrix
• Numerical ranges, Poncelet curves, invariant measures

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