Polynomials in Control Theory Parametrized by Their Roots
Joint Authors
Cisneros-Molina, José Luis
Aguirre-Hernández, Baltazar
Frías-Armenta, Martín-Eduardo
Source
International Journal of Mathematics and Mathematical Sciences
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-19, 19 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-12-24
Country of Publication
Egypt
No. of Pages
19
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Aguirre-Hernández, Baltazar& Cisneros-Molina, José Luis& Frías-Armenta, Martín-Eduardo. 2012. Polynomials in Control Theory Parametrized by Their Roots. International Journal of Mathematics and Mathematical Sciences،Vol. 2012, no. 2012, pp.1-19.
https://search.emarefa.net/detail/BIM-483686
Modern Language Association (MLA)
Aguirre-Hernández, Baltazar…[et al.]. Polynomials in Control Theory Parametrized by Their Roots. International Journal of Mathematics and Mathematical Sciences No. 2012 (2012), pp.1-19.
https://search.emarefa.net/detail/BIM-483686
American Medical Association (AMA)
Aguirre-Hernández, Baltazar& Cisneros-Molina, José Luis& Frías-Armenta, Martín-Eduardo. Polynomials in Control Theory Parametrized by Their Roots. International Journal of Mathematics and Mathematical Sciences. 2012. Vol. 2012, no. 2012, pp.1-19.
https://search.emarefa.net/detail/BIM-483686
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-483686