  We propose a numerical linear algebra based method to find the multiplication
operators of the quotient ring $\mathbb{C}[x]/I$ associated to a
zero-dimensional ideal $I$ generated by $n$ $\mathbb{C}$-polynomials in $n$
variables. We assume that the polynomials are generic in the sense that the
number of solutions in $\mathbb{C}^n$ equals the B\'ezout number. The main
contribution of this paper is an automated choice of basis for
$\mathbb{C}[x]/I$, which is crucial for the feasibility of normal form methods
in finite precision arithmetic. This choice is based on numerical linear
algebra techniques and governed by the numerical properties of the given
generators of $I$.
