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I'm learning about Vandermonde matrix to get monomial basis.

Suppose I have 4 points $(-1, 2),~ (0,7),~ (1,22) $ and $ (2,71)$

I was taught how to create the Vandermonde matrix using arbitrary numbers: $$\begin{bmatrix}1 &&x^1&& x^2 &&x^3&&\dots&& x^n\\ 1 &&y^1&& y^2 &&y^3 &&\dots&&y^n\\ 1&& z^1&& z^2&& z^3 &&\dots&&z^n\\ 1&& r^1&& r^2&& r^3&&\dots&& r^n\end{bmatrix}$$

where n = number of points - 1. I'm not sure if I was taught this correctly.

Is this the Vandermonde matrix, given the points: $$\begin{bmatrix}1&& 1&& -1&& 1\\ 1 &&0 &&0 &&0\\ 1 &&1 && 1 &&1\\ 1&& 2&& 4 &&8\end{bmatrix}$$

Certainly not a dog
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user2272600
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  • Well I guess you may not have been taught this particular properly if you were just given a vague definition and hurried along – Certainly not a dog Dec 03 '19 at 01:57
  • @Certainlynotadog I really don't think I was, my teacher tends to teach vaguely and self-learn to an extent.Is this vandermonde matrix correct for 4 points? I know how to do it with 3. – user2272600 Dec 03 '19 at 01:59
  • Actually it’s not exactly correct. For $x$ coordinates we have $$\begin{bmatrix}1&&-1&&1&&-1\1&&0&&0&&0\1&&1&&1&&1\1&&2&&4&&8\end{bmatrix}$$. And, I’m not sure if the third row is correct. It’s possible it’s undefined since the first element could be $0^0$. – Certainly not a dog Dec 03 '19 at 11:09

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