Definition:Vandermonde Determinant/Formulation 1/Also presented as/Ones at Right
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Definition
The Vandermonde determinant of order $n$ can be presented in various orientations, for example:
- $V_n = \begin {vmatrix} {x_1}^{n - 1} & {x_1}^{n - 2} & \cdots & x_1 & 1 \\ {x_2}^{n - 1} & {x_2}^{n - 2} & \cdots & x_2 & 1 \\ \vdots & \vdots & \ddots & \vdots & \vdots \\ {x_n}^{n - 1} & {x_n}^{n - 2} & \cdots & x_n & 1 \\ \end {vmatrix}$
Also see
- Results about the Vandermonde determinant can be found here.
Source of Name
This entry was named for Alexandre-Théophile Vandermonde.
Sources
- 1955: L. Mirsky: An Introduction to Linear Algebra: $\text I, \ \S 1.4: \ 1.4.5$