Derivation as operator/Linear/Eigenvectors/Exercise

Let ${}V$ denote the real vector space, which consists of all functions from ${}\mathbb {R}$ tp ${}\mathbb {R}$, which are arbitrarily often differentiable.

a) Show that the derivation ${}f\mapsto f'$ is a linear mapping from ${}V$ to ${}V$.

b) Determine the eigenvalues of the derivation and determine, for each eigenvalue, at least one eigenvector.

c) Determine for every real number the eigenspace and its

dimension.

Create a solution