Generalized Vandermonde matrix ($A_{ij}={\varphi }_{j-1}(x_{i-1})$)

A generalized Vandermonde matrix evaluates a chosen list of functions ${\varphi }_0,\dots ,{\varphi }_n$ at interpolation nodes $x_0,\dots ,x_n$. 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.