  In 1853 Sylvester stated and proved an elegant formula that expresses the
polynomial subresultants in terms of the roots of the input polynomials.
Sylvester's formula was also recently proved by Lascoux and Pragacz by using
multi-Schur functions and divided differences. In this paper, we provide an
elementary proof that uses only basic properties of matrix multiplication and
Vandermonde determinants.
