# 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 the unperturbed & perturbed matrices, as well as, spectrum of the unperturbed matrix only. The results presented give tighter bounds than the Davis-Khan sinΘ theorem. We apply the result to a graph perturbation problem.

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