Abstract:We derive new estimates for distances between optimal matchings of eigenvalues of non-normal matrices in terms of the norm of their difference. We introduce and estimate a hyperbolic metric analogue of the classical spectral-variation distance. The result yields a qualitatively new and simple characterization of the localization of eigenvalues. Our bound improves on the best classical spectralvariation bounds due to Krause if the distance of matrices is sufficiently small and is sharp for asymptotically large … Show more
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