Diagonalizable map from f to f'

[maggie56]

Homework Statement

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 don't know how to write D as a matrix.

Homework Equations

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.