Linear transformation f:C^∞(R) -> C^∞(R)(adsbygoogle = window.adsbygoogle || []).push({});

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.

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# Eigenspace and dimension

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