# Eigenspace and dimension

1. Nov 25, 2012

### Tala.S

Linear transformation f:C^∞(R) -> C^∞(R)

f(x(t)) = x'(t)

a) I have to set up the eigenvalue-problem and solve it :

My solution : ke^λt

b) Now I have to find the dimension of the single eigen spaces when λ is

-5 and 0.

My solution :

Eigenspaces :

E-5 = ke^-5t

E0=k (because ke^0t = k)

But I don't know how to find the dimension of the single eigen spaces ?

I'm used to working with vectors but now it's functions and I'm not sure about the dimension.

Last edited: Nov 25, 2012
2. Nov 27, 2012

### Tala.S

Re: Eigenspace and dimension (solved)

Solved !

3. Nov 27, 2012

### HallsofIvy

Staff Emeritus
Good! I presume that you realized that since every solution, $Ce^{\lambda x}$ is a constant, C, times the single function $e^{\lambda x}$, the space is one dimensional.