Computing the determinantal representations of hyperbolic forms

Title:

Computing the determinantal representations of hyperbolic forms

Creator:

Ming-Chih Chien and Nakazato, Hiroshi

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:19593732-0037-4c57-9ed1-a85a3fa9a619
uuid:19593732-0037-4c57-9ed1-a85a3fa9a619
issn:0011-4642

Subject:

matematika, mathematics, determinantal representation, hyperbolic form, Riemann theta function, numerical range, 13, and 51

Type:

model:article and TEXT

Format:

print, bez média, and svazek

Description:

The numerical range of an n × n matrix is determined by an n degree hyperbolic ternary form. Helton-Vinnikov confirmed conversely that an n degree hyperbolic ternary form admits a symmetric determinantal representation. We determine the types of Riemann theta functions appearing in the Helton-Vinnikov formula for the real symmetric determinantal representation of hyperbolic forms for the genus g = 1. We reformulate the Fiedler-Helton-Vinnikov formulae for the genus g = 0, 1, and present an elementary computation of the reformulation. Several examples are provided for computing the real symmetric matrices using the reformulation., Mao-Ting Chien, Hiroshi Nakazato., and Obsahuje seznam literatury

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

633-651

Source:

Czechoslovak Mathematical Journal | 2016 Volume:66 | Number:3

Harvested from:

CDK

Metadata only:

false