# Category:Examples of Vandermonde Matrix Identity

This category contains examples of use of Vandermonde Matrix Identity for Cauchy Matrix.

Assume values $\set { x_1,\ldots,x_n,y_1,\ldots,y_n }$ are distinct in matrix

 $\displaystyle C$ $=$ $\displaystyle \paren {\begin{smallmatrix} \dfrac {1} {x_1 - y_1} & \dfrac {1} {x_1 - y_2} & \cdots & \dfrac {1} {x_1 - y_n} \\ \dfrac {1} {x_2 - y_1} & \dfrac 1 {x_2 - y_2} & \cdots & \dfrac {1} {x_2 - y_n} \\ \vdots & \vdots & \cdots & \vdots \\ \dfrac {1} {x_n - y_1} & \dfrac {1} {x_n - y_2} & \cdots & \dfrac {1} {x_n - y_n} \\ \end{smallmatrix} }$ Cauchy matrix of order $n$

Then:

 $\displaystyle C$ $=$ $\displaystyle -P V_x^{-1} V_y Q^{-1}$ Vandermonde matrix identity for a Cauchy matrix

## Pages in category "Examples of Vandermonde Matrix Identity"

The following 5 pages are in this category, out of 5 total.