Inverse Numerical Range and Determinantal Quartic Curves

Mao-Ting Chien and Hiroshi Nakazato
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Mao-Ting Chien: Department of Mathematics, Soochow University, Taipei 11102, Taiwan
Hiroshi Nakazato: Department of Mathematics and Physics, Faculty of Science and Technology, Hirosaki University, Hirosaki 036-8561, Japan

Mathematics, 2020, vol. 8, issue 12, 1-10

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.

Keywords: numerical range; kernel vector function; theta function; quartic curve (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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