Computing real definite representations of Helton-Vinnikov theorem

DOI10.1007/s43037-021-00169-zzbMath1478.15032OpenAlexW4206511914MaRDI QIDQ2073140

Mao-Ting Chien, Hiroshi Nakazato

Publication date: 27 January 2022

Published in: Banach Journal of Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s43037-021-00169-z

zbMATH Keywords

Riemann theta functionnumerical rangeAbel-Jacobi mapreal definite representation

Mathematics Subject Classification ID

Determinants, permanents, traces, other special matrix functions (15A15) Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Numerical range, numerical radius (47A12) Computational aspects of algebraic curves (14Q05) Theta functions and curves; Schottky problem (14H42)

Related Items (1)

Theta divisor and Abel map for 4-by-4 matrices

Uses Software

• Maple

Cites Work

• Determinantal representation of trigonometric polynomial curves via Sylvester method
• Reduction of the \(c\)-numerical range to the classical numerical range
• Pencils of real symmetric matrices and real algebraic curves
• Self-adjoint determinantal representations of real plane curves
• Unitary similarity of the determinantal representation of unitary bordering matrices
• Higher-rank numerical ranges and Kippenhahn polynomials
• Computing Linear Matrix Representations of Helton-Vinnikov Curves
• The possible shapes of numerical ranges
• Combinatorial group theory, Riemann surfaces and differential equations
• Differential equations, difference equations and matrix theory
• Linear matrix inequality representation of sets
• Toeplitz matrices are unitarily similar to symmetric matrices
• Über den Wertevorrat einer Matrix

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