Generalized Vandermonde matrix
= Generalized Vandermonde matrix
{title2=$A_{ij}=\phi_{j-1}(x_{i-1})$}
A generalized Vandermonde matrix evaluates a chosen list of <functions> $\phi_0,\ldots,\phi_n$ at <interpolation nodes> $x_0,\ldots,x_n$. For a <basis> of <polynomials> of <polynomial degree> at most $n$ and distinct nodes, it is an <invertible matrix> by uniqueness of <polynomial interpolation>. Choosing monomials recovers the ordinary <Vandermonde matrix>.