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This manuscript presents a generalization of the structure of the null spaceof the Bezout matrix in the monomial basis, see [G. Heinig and K. Rost,Algebraic methods for toeplitz-like matrices and operators, 1984], to anarbitrary basis. In addition, two methods for computing the gcd of severalpolynomials, using also Bezout matrices, without having to convert them to themonomial basis. The main point is that the presented results are expressed withrespect to an arbitrary polynomial basis. In recent years, many problems inpolynomial systems, stability theory, CAGD, etc., are solved using Bezoutmatrices in distinct specific bases. Therefore, it is very useful to haveresults and tools that can be applied to any basis.

The null space of the Bezout matrix in any basis and gcd's