_matrix">Vandermonde matrix</Span></a> and it comes from the simple fact that if a polynomial runs through a point <i>(x<sub>i</sub>, y<sub>i</sub>)</i> then <i>P(x<sub>i</sub>) = y<sub>i</sub></i>. Just write this down for every point, put it into the matrix form and here you go.
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One widely known fact is you can't have your polynomial degree less than the number of points minus one. Another less known fact is that you can have it greater. It's very easy to see. Just imagine adding an extra point