Definition:Vandermonde Matrix/Formulation 2

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The Vandermonde matrix of order $n$ is a square matrix specified variously as:

$\begin {bmatrix}

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

That is, such that:

$a_{i j} = {x_j}^i$

Also known as

A Vandermonde matrix is often seen referred to as Vandermonde's matrix.

The first form is preferred on $\mathsf{Pr} \infty \mathsf{fWiki}$ because it is slightly less grammatically unwieldy than the possessive style.

Also see

  • Results about Vandermonde matrices can be found here.

Source of Name

This entry was named for Alexandre-Théophile Vandermonde.