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2014 Determinantal representation of trigonometric polynomial curves via Sylvester method
Mao-Ting Chien, Hiroshi Nakazato
Banach J. Math. Anal. 8(1): 269-278 (2014). DOI: 10.15352/bjma/1381782099

Abstract

For any trigonometric polynomial $\phi(\theta)$, we give a constructive algorithm by Sylvester elimination which produces matrices $C_1, C_2, C_3$ such that $\det(C_1+ \Re(\phi(\theta)) C_2+ \Im(\phi(\theta)) C_3)=0.$ For a typical trigonometric polynomial, we assert that $C_1$ is positive definite, and thus the typical polynomial curve admits

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Mao-Ting Chien. Hiroshi Nakazato. "Determinantal representation of trigonometric polynomial curves via Sylvester method." Banach J. Math. Anal. 8 (1) 269 - 278, 2014. https://doi.org/10.15352/bjma/1381782099

Information

Published: 2014
First available in Project Euclid: 14 October 2013

zbMATH: 1283.15025
MathSciNet: MR3161694
Digital Object Identifier: 10.15352/bjma/1381782099

Subjects:
Primary: 47A10
Secondary: 47A12

Keywords: determinantal representation , numerical range , Sylvester method

Rights: Copyright © 2014 Tusi Mathematical Research Group

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Vol.8 • No. 1 • 2014
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