Controllability, Bezoutian and relative primeness
Let f(x) and g(x) be two polynomials of degree n. Then it is well-known that the Bezoutian matrix Bfg associated with f(x) and g(x) is nonsingular if and only if f(x) and g(x) are relatively prime. We give an alternative proof of this result. The proof is based on a result on controllability derived...
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| Format: | Article |
| Language: | English |
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Wiley
1980-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171280000129 |
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| author | B. N. Datta |
| author_facet | B. N. Datta |
| author_sort | B. N. Datta |
| collection | DOAJ |
| description | Let f(x) and g(x) be two polynomials of degree n. Then it is well-known that the Bezoutian matrix Bfg associated with f(x) and g(x) is nonsingular if and only if f(x) and g(x) are relatively prime. We give an alternative proof of this result. The proof is based on a result on controllability derived in this note. |
| format | Article |
| id | doaj-art-075f69201c7e41409c4872250da1b720 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1980-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-075f69201c7e41409c4872250da1b7202025-02-03T05:46:58ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251980-01-013118518810.1155/S0161171280000129Controllability, Bezoutian and relative primenessB. N. Datta0Instituto de Matemática, Estatistica e Ciência da Computaçgão, Universidade Estadual de Campinas, Campinas, SP, BrazilLet f(x) and g(x) be two polynomials of degree n. Then it is well-known that the Bezoutian matrix Bfg associated with f(x) and g(x) is nonsingular if and only if f(x) and g(x) are relatively prime. We give an alternative proof of this result. The proof is based on a result on controllability derived in this note.http://dx.doi.org/10.1155/S0161171280000129Bezoutiancontrollabilitynullity. |
| spellingShingle | B. N. Datta Controllability, Bezoutian and relative primeness International Journal of Mathematics and Mathematical Sciences Bezoutian controllability nullity. |
| title | Controllability, Bezoutian and relative primeness |
| title_full | Controllability, Bezoutian and relative primeness |
| title_fullStr | Controllability, Bezoutian and relative primeness |
| title_full_unstemmed | Controllability, Bezoutian and relative primeness |
| title_short | Controllability, Bezoutian and relative primeness |
| title_sort | controllability bezoutian and relative primeness |
| topic | Bezoutian controllability nullity. |
| url | http://dx.doi.org/10.1155/S0161171280000129 |
| work_keys_str_mv | AT bndatta controllabilitybezoutianandrelativeprimeness |