Linear transformation f:C^{∞}(R) -> C^{∞}(R)
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 and plot the graph for 3 different vectors from each eigen space when λ is
-5 and 0.
I'm having some problems with this part. I I've chosen k as 2, 5 and 13 and then I just plot them with the two different λ values :
k = 2
2e^{-5}^{t}
2e^{0t} = 2
k = 5
5e^{-5}^{t}
5e^{0}^{t} = 5
k = 13
13e^{-5}^{t}
13e^{0}^{t} = 13
Eigenspaces :
E_{-5} = ke^{-5t }
E_{0}=k
But I don't know how to find the dimension of the single eigen spaces ?