Controllability, Bezoutian and relative primeness - B. N. Datta (International Journal of Mathematics and Mathematical Sciences)
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.