Bézout matrix (awaiting review)

Given two polynomials $f$ and $g$ of degree at most $n$, their degree $n$ Bézout matrix is the $n\times n$ matrix $(c_{ij})$ where \[ \frac{f(x)g(y)-f(y)g(x)}{x-y} = \sum_{i,j=1}^n c_{ij} x^i y^{j}.\] The determinant of this matrix is the resultant of the two polynomials.