Value of Vandermonde Determinant

Theorem
The Vandermonde determinant of order $n$ is the determinant defined as follows:


 * $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}$

Its value is given by:
 * $\displaystyle V_n = \prod_{1 \mathop \le i \mathop < j \mathop \le n} \paren {x_j - x_i}$