1. The problem statement, all variables and given/known data Let U be the R-vector space consisting of all polynomials of degree at most n with coefficients that are real. The Derivative Map F : U [tex]\rightarrow[/tex] U f(x) [tex]\rightarrow[/tex] f'(x) Is the derivative function F diagonalizable? 3. The attempt at a solution My instinct says yes but I'm not too sure why. Am I right in saying that eigenvalues are invariant after a linear transform. I'm pretty sure that before the function is applied you can have a matrix that has n+1 distinct eignenvalues but not sure if this is the right lines or if it is how to set about writing it down in a proof format. Any help would be great thanks !