Definition:Vandermonde Matrix/Formulation 1

Definition
The Vandermonde matrix of order $n$ is a square matrix specified variously as:
 * $\begin {bmatrix}

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 {bmatrix}$

That is, such that:
 * $a_{i j} = {x_i}^{j - 1}$

Also see

 * Definition:Vandermonde Matrix/Formulation 2
 * Definition:Vandermonde Determinant