International Journal of Mathematics and Mathematical Sciences
Volume 3 (1980), Issue 1, Pages 185-188
doi:10.1155/S0161171280000129
Controllability, Bezoutian and relative primeness
Instituto de Matemática, Estatistica e Ciência da Computaçgão, Universidade Estadual de Campinas, Campinas, SP, Brazil
Received 11 June 1979
Copyright © 1980 B. N. Datta. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
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.