Numerical ranges of the real \(2\times 2\) matrices derived by first principles

DOI10.7546/GIQ-24-2022-65-83MaRDI QIDQ6158497

Ivaïlo M. Mladenov, Clementina D. Mladenova

Publication date: 31 May 2023

Published in: Geometry, Integrability and Quantization (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/journals/geometry-integrability-and-quantization-papers-and-lecture-series/volume-24/issue-none/Numerical-Ranges-of-the-Real-2times-2-Matrices-Derived-by/10.7546/giq-24-2022-65-83.full

zbMATH Keywords

numerical rangefield of valuesmatrix theoryparameterizationenveloping curveCassinian ovalsJacobi's method for diagonalization

Mathematics Subject Classification ID

Numerical range, numerical radius (47A12) Miscellaneous inequalities involving matrices (15A45)

Cites Work

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• Cayley map for symplectic groups
• New parameterizations of \(\mathrm{SL}(2,\mathbb{R})\) and some explicit formulas for its logarithm
• The many faces of elastica
• The spiric sections of Perseus and the uniform parameterizations of the Cassinian ovals
• Analytical descriptions of Perseus spirics
• The rectifications of the Cassinian ovals: third round
• Limits for the characteristic roots of a matrix. II
• On Some Deformations of the Cassinian Oval
• Computation of the field of values of a 2 x 2 matrix
• On the numerical range of a matrix
• Cassini Ovals Associated with a Second Order Matrix
• New and old parameterizations of the Cassinian ovals and some applications of them

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