Proving that the adjoint of a general linear operator times said operator is a Hermitian on a complex vector space

Question

With L being a linear operator on a complex vector space $V$ show that $L^{_\dagger}L$ is Hermitian with non negative eigenvalues

I don't really have much of an idea how to do this exercise in such a general example. The proof of non negative eigenvalues is especially eluding me. Any ideas?