Category:Definitions/Vandermonde Determinant

This category contains definitions related to Vandermonde Determinant.
Related results can be found in Category:Vandermonde Determinant.

The Vandermonde determinant of order $n$ is the determinant defined as one of the following two formulations:

Formulation 1

$V_n = \begin {vmatrix}

1 & x_1 & {x_1}^2 & \cdots & {x_1}^{n - 2} & {x_1}^{n - 1} \\ 1 & x_2 & {x_2}^2 & \cdots & {x_2}^{n - 2} & {x_2}^{n - 1} \\ \vdots & \vdots & \vdots & \ddots & \vdots & \vdots \\ 1 & x_n & {x_n}^2 & \cdots & {x_n}^{n - 2} & {x_n}^{n - 1} \end {vmatrix}$

Formulation 2

$V_n = \begin {vmatrix}

x_1 &  {x_1}^2 & \cdots &  {x_1}^n \\
x_2 &  {x_2}^2 & \cdots &  {x_2}^n \\

\vdots & \vdots & \ddots & \vdots \\

x_n &  {x_n}^2 & \cdots &  {x_n}^n

\end{vmatrix}$