(Question) What is the (conventional) formula for coefficients of interpolation polynomial?
Consider the interpolation problem: find the polynomial through a given set of points $(x_0,y_0),...,(x_n,y_n)$. Suppose we want the polynomial in canonical form (monomial basis): coefficients times powers of $x$.
Is there a standard solution to this problem? What would be the formula for the coefficients and how is it obtained?
Note: I found my own solutions for this problem, but I would like to know the ‘standard’ solution. Maybe it involves some Linear Algebra that I am not aware of yet.