A Geometric Approach to Computing Bounds on Perturbations of Invariant Subspaces of Normal Matrices with Application to a Graph Connection Problem

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 (1) spectrum of both the unperturbed and perturbed matrices, as well as, (2) spectrum of the unperturbed matrix only. The results presented give sightly tighter bounds than the Davis-Khan $\sin\Theta$ theorem. We apply the result to a graph perturbation problem.