Vandermonde Determinant

Author

Eric W. Weisstein
October 1, 2002

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

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

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

Initialization

<<DiscreteMath`Combinatorica`;

Code

Vandermonde[a_List?VectorQ]:=Outer[Power,a,Range[Length[a]]-1]

Determinant

Table[FullSimplify[Det[Vandermonde[Array[x,n]]]]/.x[k_]:>Subscript[x,k],{n,5}]//ColumnForm//TraditionalForm

Table[Times@@Subtract@@@(Reverse/@KSubsets[Array[x,n],2])-Det[Vandermonde[Array[x,n]]],{n,6}]//Simplify

Table[(-1)^Floor[n/2]Times@@Subtract@@@KSubsets[Array[x,n],2]-Det[Vandermonde[Array[x,n]]],{n,6}]//Simplify