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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Hindawi Limited
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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doaj-075f69201c7e41409c4872250da1b7202020-11-24T22:08:32ZengHindawi LimitedInternational 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. |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
B. N. Datta |
| spellingShingle |
B. N. Datta Controllability, Bezoutian and relative primeness International Journal of Mathematics and Mathematical Sciences Bezoutian controllability nullity. |
| author_facet |
B. N. Datta |
| author_sort |
B. N. Datta |
| title |
Controllability, Bezoutian and relative primeness |
| title_short |
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_sort |
controllability, bezoutian and relative primeness |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
1980-01-01 |
| 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. |
| topic |
Bezoutian controllability nullity. |
| url |
http://dx.doi.org/10.1155/S0161171280000129 |
| work_keys_str_mv |
AT bndatta controllabilitybezoutianandrelativeprimeness |
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