Answer by achille hui for Why are Vandermonde matrices invertible?
For any $n+1$ distinct numbers $x_0, \ldots, x_n \in \mathbb{R}$, let $V(x_0,\ldots,x_n)$ and $D(x_0,\ldots,x_n)$ be a Vandermonde matrix and its determinant:$$V(x_0,\ldots,x_n) = \begin{pmatrix} x_0^0...
View ArticleAnswer by Martin Sleziak for Why are Vandermonde matrices invertible?
This is not entirely dissimilar to the answer already posted by Chris Godsil, but I'll post this anyway, maybe it can provide slightly different angle for someone trying to understand this.We want to...
View ArticleAnswer by Chris Godsil for Why are Vandermonde matrices invertible?
Let $V$ be your Vandermonde matrix. If $p(t)=a_0+a_1t+\cdots+a_nt^n$ and $\alpha$ is the vector of coefficients of $p$, then the entries of $V\alpha$ are the values of $p$ on the points...
View ArticleWhy are Vandermonde matrices invertible?
A Vandermonde-matrix is a matrix of this form:$$\begin{pmatrix} x_0^0 & \cdots & x_0^n \\\vdots & \ddots & \vdots \\ x_n^0 & \cdots & x_n^n\end{pmatrix} \in \mathbb{R}^{(n+1)...
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