Definition:Vandermonde Matrix/Formulation 2
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Definition
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.
Sources
- 1997: Donald E. Knuth: The Art of Computer Programming: Volume 1: Fundamental Algorithms (3rd ed.) ... (previous) ... (next): $\S 1.2.3$: Sums and Products: Exercises -- Second Set