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International Journal of Mathematics and Mathematical Sciences
Volume 3, 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 Hindawi Publishing Corporation. 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 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.