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 spectrum of the unperturbed matrix only. We apply the result to a graph perturbation problem.