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## Homework Statement

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?

## 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 !