A proof of Crouzeix's conjecture for a class of matrices

DOI10.1016/j.laa.2012.12.045zbMath1281.15021OpenAlexW2083039183WikidataQ123149228 ScholiaQ123149228MaRDI QIDQ1947088

Daeshik Choi

Publication date: 12 April 2013

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

Full work available at URL: https://doi.org/10.1016/j.laa.2012.12.045

zbMATH Keywords

numerical rangematrix polynomialsmatrix normsJordan blocksCrouzieix's conjecture

Mathematics Subject Classification ID

Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Numerical range, numerical radius (47A12)

Related Items (12)

Variational analysis of the Crouzeix ratio ⋮ An Algorithm for Finding a 2-Similarity Transformation from a Numerical Contraction to a Contraction ⋮ The Numerical Range is a $(1+\sqrt{2})$-Spectral Set ⋮ Between the von Neumann inequality and the Crouzeix conjecture ⋮ Crouzeix's Conjecture Holds for Tridiagonal 3 x 3 Matrices with Elliptic Numerical Range Centered at an Eigenvalue ⋮ Numerical range and compressions of the shift ⋮ Crouzeix's conjecture and related problems ⋮ Some Extensions of the Crouzeix--Palencia Result ⋮ Numerical investigation of Crouzeix's conjecture ⋮ Some Constants Related to Numerical Ranges ⋮ Approximating the leading singular triplets of a large matrix function ⋮ Characterization of half-radial matrices

Cites Work

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• Numerical range and functional calculus in Hilbert space
• Bounds for analytical functions of matrices
• Crouzeix's conjecture and perturbed Jordan blocks
• Eine Spektraltheorie für allgemeine Operatoren eines unitären Raumes. Erhard Schmidt zum 75. Geburtstag in Verehrung gewidmet

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