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Inverse Numerical Range and Determinantal Quartic Curves

Author

Listed:
  • Mao-Ting Chien

    (Department of Mathematics, Soochow University, Taipei 11102, Taiwan
    These authors contributed equally to this work.)

  • Hiroshi Nakazato

    (Department of Mathematics and Physics, Faculty of Science and Technology, Hirosaki University, Hirosaki 036-8561, Japan
    These authors contributed equally to this work.)

Abstract

A hyperbolic ternary form, according to the Helton–Vinnikov theorem, admits a determinantal representation of a linear symmetric matrix pencil. A kernel vector function of the linear symmetric matrix pencil is a solution to the inverse numerical range problem of a matrix. We show that the kernel vector function associated to an irreducible hyperbolic elliptic curve is related to the elliptic group structure of the theta functions used in the Helton–Vinnikov theorem.

Suggested Citation

  • Mao-Ting Chien & Hiroshi Nakazato, 2020. "Inverse Numerical Range and Determinantal Quartic Curves," Mathematics, MDPI, vol. 8(12), pages 1-10, November.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:12:p:2119-:d:451834
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