VMath matrix_e
http://vmath.ru/vf5/
2026-10-13T04:35:57+0300VMath
http://vmath.ru/vf5/
http://vmath.ru/vf5/lib/tpl/vf5/images/favicon.icotext/html2023-07-01T15:01:46+0300Anonymous (anonymous@undisclosed.example.com)Vandermonde's matrix and determinant
http://vmath.ru/vf5/matrix_e/vander_e?rev=1688212906&do=diff
Author---Русская версия
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Vandermonde's matrix and determinant
Let the system of numbers (elements of a field) $ \{x_1,x_2,\dots,x_n \} $ be given, not necessarily distinct.
Matrix of the form
$$
\mathbf V_{m\times n}(x_1, x_2,\ldots,x_n) =
\left(
\begin{array}{llll}
1& 1& \ldots& 1\\
x_1& x_2& \ldots& x_n\\
x_1^2& x_2^2& \ldots& x_n^2\\
\vdots& \vdots& & \vdots \\
x_1^{m-1}& x_2^{m-1}& \ldots& x_n^{m-1}
\end{array}
\right)_{m\times n}
$$
or its transpose is called $ m \tim…