Crouzeix's Conjecture Holds for Tridiagonal 3 x 3 Matrices with Elliptic Numerical Range Centered at an Eigenvalue

DOI10.1137/17M1110663zbMath1383.15019arXiv1701.01365WikidataQ123302319 ScholiaQ123302319MaRDI QIDQ4604570

Christer Glader, Mikael Kurula, Mikael Lindström

Publication date: 2 March 2018

Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1701.01365

zbMATH Keywords

eigenvalueelliptic numerical rangeCrouzeix's conjecture\({3 \times 3}\) matrix

Mathematics Subject Classification ID

Eigenvalues, singular values, and eigenvectors (15A18) Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60)

Related Items (4)

On the uniqueness of functions that maximize the Crouzeix ratio ⋮ Numerical range and compressions of the shift ⋮ Crouzeix's conjecture and related problems ⋮ Some Extensions of the Crouzeix--Palencia Result

Uses Software

• Mathematica
• Maxima

Cites Work

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• The numerical range of \(3 \times 3\) matrices
• Numerical range and functional calculus in Hilbert space
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• Crouzeix's conjecture and perturbed Jordan blocks
• Some Constants Related to Numerical Ranges
• On Matrices with Elliptical Numerical Ranges
• The Numerical Range is a $(1+\sqrt{2})$-Spectral Set
• On the numerical range of a matrix
• Eine Spektraltheorie für allgemeine Operatoren eines unitären Raumes. Erhard Schmidt zum 75. Geburtstag in Verehrung gewidmet

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