Neumann Eigenvalue is Nonnegative

Theorem
Let $\struct {M, g}$ be a compact connected Riemannian manifold with non-empty boundary $\partial M$.

Let $\lambda$ be a Neumann eigenvalue of $M$.

Then $\lambda$ is nonnegative.

That is, $0$ is a Neumann eigenvalue, and all the other Neumann eigenvalues are strictly positive.