Polynomials in Control Theory Parametrized by Their Roots
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 t...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2012/595076 |
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| author | Baltazar Aguirre-Hernández José Luis Cisneros-Molina Martín-Eduardo Frías-Armenta |
| author_facet | Baltazar Aguirre-Hernández José Luis Cisneros-Molina Martín-Eduardo Frías-Armenta |
| author_sort | Baltazar Aguirre-Hernández |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-ba06a8cb1d9c465990652b1f0beee00d |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-ba06a8cb1d9c465990652b1f0beee00d2025-02-03T05:59:46ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252012-01-01201210.1155/2012/595076595076Polynomials in Control Theory Parametrized by Their RootsBaltazar Aguirre-Hernández0José Luis Cisneros-Molina1Martín-Eduardo Frías-Armenta2Departamento de Matemáticas, División de Ciencias Básicas e Ingeniería, Universidad Autónoma Metropolitana-Iztapalapa, Avenida San Rafael Atlixco no. 186, Colonia Vicentina, 09340 Mexico, DF, MexicoInstituto de Matemáticas, Unidad Cuernavaca, Universidad Nacional Autónoma de México, Avenida Universidad s/n, Colonia Lomas de Chamilpa, 62210 Cuernavaca, MOR, MexicoDepartamento de Matemáticas, División de Ciencias Exactas, Universidad de Sonora, Boulevard Luis Encinas y Rosales s/n, Colonia Centro, 83000 Hermosillo, SON, MexicoThe 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.http://dx.doi.org/10.1155/2012/595076 |
| spellingShingle | Baltazar Aguirre-Hernández José Luis Cisneros-Molina Martín-Eduardo Frías-Armenta Polynomials in Control Theory Parametrized by Their Roots International Journal of Mathematics and Mathematical Sciences |
| title | Polynomials in Control Theory Parametrized by Their Roots |
| title_full | Polynomials in Control Theory Parametrized by Their Roots |
| title_fullStr | Polynomials in Control Theory Parametrized by Their Roots |
| title_full_unstemmed | Polynomials in Control Theory Parametrized by Their Roots |
| title_short | Polynomials in Control Theory Parametrized by Their Roots |
| title_sort | polynomials in control theory parametrized by their roots |
| url | http://dx.doi.org/10.1155/2012/595076 |
| work_keys_str_mv | AT baltazaraguirrehernandez polynomialsincontroltheoryparametrizedbytheirroots AT joseluiscisnerosmolina polynomialsincontroltheoryparametrizedbytheirroots AT martineduardofriasarmenta polynomialsincontroltheoryparametrizedbytheirroots |