Editing Vandermonde matrix (section)

== Inverse Vandermonde matrix ==
As explained above in Applications, the [[polynomial interpolation]] problem for <math>p(x) = a_0 + a_1 x + a_2 x^2 + \dots + a_n x^n</math>satisfying <math>p(x_0)=y_0, \ldots,p(x_n)=y_n</math> is equivalent to the matrix equation <math>Va = y</math>, which has the unique solution <math>a = V^{-1}y</math>. There are other known formulas which solve the interpolation problem, which must be equivalent to the unique  <math>a = V^{-1}y</math>, so they must give explicit formulas for the inverse matrix <math>V^{-1}</math>. In particular, [[Lagrange polynomial|Lagrange interpolation]] shows that the columns of the inverse matrix 

<math display="block">V^{-1}=
\begin{bmatrix}
1 & x_0 & \dots & x_0^n\\
\vdots & \vdots &  &\vdots \\[.5em]
1 & x_n & \dots & x_n^n
\end{bmatrix}^{-1}