UB-matrices and conditions for Poncelet polygon to be closed

DOI10.1016/S0024-3795(02)00447-0zbMath1028.15025MaRDI QIDQ1863525

Boris Mirman

Publication date: 11 March 2003

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

zbMATH Keywords

eigenvalueseigenvectornumerical rangePoncelet's porismunitary dilationUB-matrix

Mathematics Subject Classification ID

Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Hermitian, skew-Hermitian, and related matrices (15B57)

Related Items (21)

Reducibility of the ternary forms of unitary bordering matrices ⋮ Which set is the numerical range of an operator? ⋮ Numerical range of a normal compression. II ⋮ Poncelet's theorem, Sendov's conjecture, and Blaschke products ⋮ Numerical Range of a Normal Compression ⋮ Singular points of the algebraic curves associated to unitary bordering matrices ⋮ Interior and exterior curves of finite Blaschke products ⋮ Poncelet's porism in the finite real plane ⋮ Poncelet-Darboux, Kippenhahn, and Szegő: interactions between projective geometry, matrices and orthogonal polynomials ⋮ Poncelet's theorem, paraorthogonal polynomials and the numerical range of compressed multiplication operators ⋮ Numerical Ranges of Operators and Matrices ⋮ Decomposable Blaschke products of degree 2ⁿ ⋮ Explicit solutions to Poncelet's porism ⋮ Crouzeix's conjecture and related problems ⋮ Short cycles of Poncelet's conics ⋮ Decomposing finite Blaschke products ⋮ On foci of ellipses inscribed in cyclic polygons ⋮ Numerical range circumscribed by two polygons ⋮ Norms of truncated Toeplitz operators and numerical radii of restricted shifts ⋮ A characterization of complex plane Poncelet curves ⋮ Four Theorems with Their Foci on Ellipses

Cites Work

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• On the numerical range of a bounded operator
• Poncelet's closure theorem
• On inscribed circumscribed conics
• A Poncelet theorem in space
• On Cayley's explicit solution to Poncelet's porism
• Numerical ranges and Poncelet curves
• Polygons and Numerical Ranges
• Numerical range ofs(φ)
• Geometry. I, II. Transl. from the French by M. Cole and S. Levy
• Numerical ranges, Poncelet curves, invariant measures

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