International Journal of Mathematics and Mathematical Sciences
Volume 3 (1980), Issue 1, Pages 185-188
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.
Let and be two polynomials of degree . Then it is well-known that the Bezoutian matrix associated with and is nonsingular if and only if and are relatively prime. We give an alternative proof of this result. The proof is based on a result on controllability derived in this note.