diagonalizable map from f to f'

maggie56

1. The problem statement, all variables and given/known data
Hi, i need to show if the map D: Vn maps Vn for f(x) maps to f '(x) is diagonalizable.
I know how to do this with matrices i am given, but i dont know how to write D as a matrix.

2. Relevant equations



3. The attempt at a solution
I'd really appreciate it if someone could give me some help.

Thanks

micromass

Some remarks:
1) what is Vn? It's common practice to explain every notation you use...
2) What did you try already? You must have done something... Did you check the definitions already, what are they? Consider some easy examples,... I mean, just writing "I'd really appreciate it if someone could give me some help." is not an attempt at a solution!!

After you've explained some more, we'll be happy to help you

fzero

You might get a better response if you define Vn and D. Is D a derivative operator? If so, it has extremely specific eigenfunctions.