Definition:Vandermonde Matrix/Formulation 1/Also presented as

Definition

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

Ones at Right

$\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}$

Ones at Top

$\begin {bmatrix}

 1 &  1  & \cdots  &   1 \\

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

Also see

• Results about Vandermonde matrices can be found here.

Source of Name

This entry was named for Alexandre-Théophile Vandermonde.