Construction of determinantal representation of trigonometric polynomials
type: Item
instance of: scholarly article
title: Construction of determinantal representation of trigonometric polynomials
zbMATH Open document ID: 1222.15008
author: Mao-Ting Chien
author: Hiroshi Nakazato
published in: Linear Algebra and its Applications
publication date: 2011-07-15T00:00:00Z
review text: For a pair of \(n\times n\) Hermitian matrices \(S_{1}\) and \(S_{2}\), a real ternary homogeneous polynomial defined by \[ F(t, x,y)=\text{det}(tI_{n}+xS_{1}+yS_{2})\tag{1} \] is hyperbolic with respect to \((1,0,0)\). The authors construct real symmetric matrices \(S_{1}\) and \(S_{2}\) satisfying (1) for a hyperbolic form \(F_{\phi}\) corresponding to a general trigonometric polynomial \(\phi\). A criterion for the associated form \(F_{\phi}\) to be hyperbolic with respect to \((1,0,0)\) is given.
reviewed by: Stamatis Koumandos
Mathematics Subject Classification ID: 15A15
Mathematics Subject Classification ID: 42A05
Mathematics Subject Classification ID: 15B57
zbMATH DE Number: 5924537
zbMATH Keywords: hyperbolic polynomial
zbMATH Keywords: real ternary homogeneous polynomial
zbMATH Keywords: trigonometric polynomial
zbMATH Keywords: Bézoutian matrix
zbMATH Keywords: determinantal representation
zbMATH Keywords: Hermitian matrices
zbMATH Keywords: real symmetric matrices
MaRDI profile type: Publication
full work available at URL: j.laa.2011.03.012
OpenAlex ID: W1983748017
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DOI: 10.1016/J.LAA.2011.03.012
description: scientific article; zbMATH DE number 5924537