On some bounds on the perturbation 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 ℂ^n in terms of the spectrum of both unperturbed and perturbed matrices as well as the spectrum of the unperturbed matrix only. The results presented give tighter bounds than the Davis–Kahan sinΘ theorem. We apply the result to a graph perturbation problem.