Generalized Vandermonde Matrix

Author

Eric W. Weisstein
October 1, 2002

This notebook downloaded from http://mathworld.wolfram.com/notebooks/LinearAlgebra/GeneralizedVandermondeMatrix.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/GeneralizedVandermondeMatrix.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Code

Vandermonde[a_List?VectorQ,b_List?VectorQ]:=Outer[Power,a,b]/;Equal@@Length/@{a,b}

Example

Vandermonde[Array[a,3],Array[b,3]]/.x_[n_]:>Subscript[x,n]//MatrixForm//TraditionalForm

FullSimplify[Det[Vandermonde[Array[a,2],Array[b,2]]]]/.x_[n_]:>Subscript[x,n]

FullSimplify[Det[Vandermonde[Array[a,3],Array[b,3]]]]/.x_[n_]:>Subscript[x,n]

FullSimplify[Det[Vandermonde[Array[a,4],Array[b,4]]]]/.x_[n_]:>Subscript[x,n]