  We provide upper bounds on the perturbation of invariant subspaces of normal
matrices measured using a metric on the space of vector subspaces of
$\mathbb{C}^n$ in terms of the spectrum of both the unperturbed \& perturbed
matrices, as well as, spectrum of the unperturbed matrix only. The results
presented give tighter bounds than the Davis-Khan $\sin\Theta$ theorem. We
apply the result to a graph perturbation problem.
