The boundary of higher rank numerical ranges

DOI10.1016/j.laa.2011.05.020zbMath1234.15007OpenAlexW2040044560MaRDI QIDQ636262

Mao-Ting Chien, Hiroshi Nakazato

Publication date: 26 August 2011

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

Full work available at URL: https://doi.org/10.1016/j.laa.2011.05.020

zbMATH Keywords

singular pointroulette curverank-\(k\)-numerical rangeflat portion

Mathematics Subject Classification ID

Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Computational aspects of algebraic curves (14Q05)

Related Items (12)

Singular points of the algebraic curves associated to unitary bordering matrices ⋮ On the boundary of rank-knumerical ranges ⋮ Strict convexity of the joint \(c\)-numerical range ⋮ A new Poncelet curve for the boundary generating curve of a numerical range ⋮ Hyperbolic forms associated with cyclic weighted shift matrices ⋮ Critical values for higher rank numerical ranges associated with roulette curves ⋮ Central force and the higher rank numerical range ⋮ Singular points of the algebraic curves of symmetric hyperbolic forms ⋮ On the boundary of weighted numerical ranges ⋮ Numerical range of a nilpotent matrix and related central force ⋮ Higher rank numerical ranges of Jordan-like matrices ⋮ The diameter and width of higher rank numerical ranges

Cites Work

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• Numerical range for orbits under a central force
• Construction of determinantal representation of trigonometric polynomials
• Reduction of the \(c\)-numerical range to the classical numerical range
• On the numerical range of a bounded operator
• Higher-rank numerical ranges and compression problems
• On matrices whose numerical ranges have circular or weak circular symmetry
• Quantum error correcting codes from the compression formalism
• Canonical forms, higher rank numerical ranges, totally isotropic subspaces, and matrix equations
• Condition for the higher rank numerical range to be non-empty
• A theorem on numerical range
• The higher rank numerical range is convex
• On the numerical range of a matrix
• Über den Wertevorrat einer Matrix

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