Polynomials in control theory parametrized by their roots
type: Item
instance of: scholarly article
title: Polynomials in control theory parametrized by their roots
zbMATH Open document ID: 1277.93028
DOI: 10.1155/2012/595076
author: Baltazar Aguirre-Hernández
author: José Luis Cisneros-Molina
author: Martín Eduardo Frías-Armenta
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2013-02-21T00:00:00Z
review text: Summary: The aim of this paper is to introduce the space of roots to study the topological properties of the spaces of polynomials. Instead of identifying a monic complex polynomial with the vector of its coefficients, we identify it with the set of its roots. Viète's map gives a homeomorphism between the space of roots and the space of coefficients and it gives an explicit formula to relate both spaces. Using this viewpoint we establish that the space of monic (Schur or Hurwitz) aperiodic polynomials is contractible. Additionally we obtain a boundary theorem.
Mathematics Subject Classification ID: 93B25
Mathematics Subject Classification ID: 12E05
zbMATH DE Number: 6137712
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/595076
OpenAlex ID: W2094829893
Wikidata QID: Q58704862
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DBLP publication ID: journals/ijmmsc/Aguirre-HernandezCF12
description: scientific article; zbMATH DE number 6137712