Translator Disclaimer
May 2017 Computation of Riemann matrices for the hyperbolic curves of determinantal polynomials
Mao-Ting Chien, Hiroshi Nakazato
Ann. Funct. Anal. 8(2): 152-167 (May 2017). DOI: 10.1215/20088752-3773229

Abstract

The numerical range of a matrix, according to Kippenhahn, is determined by a hyperbolic determinantal form of linear Hermitian matrices associated to the matrix. On the other hand, using Riemann theta functions, Helton and Vinnikov confirmed that a hyperbolic form always admits a determinantal representation of linear real symmetric matrices. The Riemann matrix of the hyperbolic curve plays the main role in the existence of real symmetric matrices. In this article, we implement computations of the Riemann matrix and the Abel–Jacobi variety of the hyperbolic curve associated to a determinantal polynomial of a matrix. Further, we prove that the lattice of the Abel–Jacobi variety is decomposed into the direct sum of two orthogonal lattices for some 4×4 Toeplitz matrices.

Citation

Download Citation

Mao-Ting Chien. Hiroshi Nakazato. "Computation of Riemann matrices for the hyperbolic curves of determinantal polynomials." Ann. Funct. Anal. 8 (2) 152 - 167, May 2017. https://doi.org/10.1215/20088752-3773229

Information

Received: 25 May 2016; Accepted: 12 August 2016; Published: May 2017
First available in Project Euclid: 14 January 2017

zbMATH: 1360.15024
MathSciNet: MR3597154
Digital Object Identifier: 10.1215/20088752-3773229

Subjects:
Primary: 15A60
Secondary: 14H55, 30F10

Rights: Copyright © 2017 Tusi Mathematical Research Group

JOURNAL ARTICLE
16 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.8 • No. 2 • May 2017
Back to Top