Polynomials in Control Theory Parametrized by Their Roots | Zendy

Baltazar AguirreHernández | Zendy; José Luis CisnerosMolina | Zendy; Martín-Eduardo Frías-Armenta | Zendy

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Polynomials in Control Theory Parametrized by Their Roots

Author(s) -

Baltazar AguirreHernández,

José Luis CisnerosMolina,

Martín-Eduardo Frías-Armenta

Publication year - 2012

Publication title -

international journal of mathematics and mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.21

H-Index - 39

eISSN - 1687-0425

pISSN - 0161-1712

DOI - 10.1155/2012/595076

Subject(s) - mathematics , monic polynomial , contractible space , homeomorphism (graph theory) , pure mathematics , boundary (topology) , space (punctuation) , polynomial , aperiodic graph , complex quadratic polynomial , discrete mathematics , algebra over a field , combinatorics , mathematical analysis , linguistics , philosophy

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

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