Category:Examples of Vandermonde Matrix Identity
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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
| \(\ds C\) | \(=\) | \(\ds \begin {pmatrix}
\dfrac 1 {x_1 - y_1} & \dfrac 1 {x_1 - y_2} & \cdots & \dfrac 1 {x_1 - y_n} \\
\dfrac 1 {x_2 - y_1} & \dfrac 1 {x_2 - y_2} & \cdots & \dfrac 1 {x_2 - y_n} \\
\vdots & \vdots & \cdots & \vdots \\
\dfrac 1 {x_n - y_1} & \dfrac 1 {x_n - y_2} & \cdots & \dfrac 1 {x_n - y_n} \\
\end {pmatrix}\) |
Cauchy matrix of order $n$ |
Then:
| \(\ds C\) | \(=\) | \(\ds -P V_x^{-1} V_y Q^{-1}\) | 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.