How to show that λ is an eigenvalue of D by finding a corresponding eigenfunction Define the _differentiation operator_ $D$ to be the transformation $D : C_\infty(\mathbb R)\to C_\infty(\mathbb R)$ given by $D( f ) = f'$. How can I show that every real number $\lambda$ is an eigenvalue of $D$ by finding a corresponding eigenfunction and what will be the dimension of its eigenspace

**Hint:** For a given number $\lambda$, consider $f(x)=e^{\lambda x}$, which is a vector in your vector space. Why is this an eigenvector? What is the associated eigenvalue?