## Franklin's Notes

### Vandermonde Matrix

A Vandermonde matrix takes the form These matrices are useful for manipulating polynomials using linear algebra. For example, if $x$ is the column vector whose entries are the values $x_i$, and $c$ is a coefficient vector then the matrix-vector multiply $Ac$ evaluates the polynomial $p$ with coefficients given by the $c_i$ at each of the points $x_i$: where $p(x)$ represents the vector whose elements are $p(x_i)$, so that the polynomial is applied elementwise.