Definition:Vandermonde Matrix/Formulation 1/Also presented as/Ones at Right

Definition

The Vandermonde matrix of order $n$ can be presented in various orientations, for example:

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

That is, such that:

$a_{i j} = {x_i}^{n - j}$

Also see

• Results about Vandermonde matrices can be found here.

Source of Name

This entry was named for Alexandre-Théophile Vandermonde.