Excercise 1 reffered to Only need answer to d
Excercise 1 (in text): Given the (complex) linear space spanned by {$\sin x$, $\cos x$, $e^{2x}$} . On this space we define the linear mapping T as the derivative, i.e. ,
$T(f) = \frac{df}{dx}$
(a) Determine the eigenvalues and eigenvectors of T.
(b) Prove that T is diagonisable.
(c) Determine the eigenvalues of the inverse of T.
Only need answer to d) as follows:
d) Let T be the operator from Exercise 1. There exists an inner product on the space spanned by {$\sin x$, $\cos x$, $e^{2x}$} such that T becomes self-adjoint or normal.