Vandermonde Matrix
Definition. The Vandermonde matrix of order $n$ is the matrix $$V = \begin{bmatrix} 1 & x_1 & x^2_1 & \cdots & x_1^{n-1} \\ 1 & x_2 & x^2_2 & \cdots & x_2^{n-1} \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ 1 & x_n & x^2_n & \cdots & x_n^{n-1} \end{bmatrix}.$$
Theorem
Theorem. The determinant of the Vandermonde matrix $V$ of order $n$ is $$\det(V) = \prod_{1 \leq i < j \leq n} (x_j - x_i).$$