A new Gershgorin‐type result for the localisation of the spectrum of matrices |
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Authors: | Anna Dall'Acqua Delio Mugnolo Michael Schelling |
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Institution: | 1. Institut für Analysis, Fakult?t für Mathematik und Wirtschaftswissenschaften, Universit?t Ulm, Ulm, Germany;2. Lehrgebiet Analysis, Fakult?t für Mathematik und Informatik, FernUniversit?t Hagen, Hagen, Germany |
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Abstract: | We present a Gershgorin's type result on the localisation of the spectrum of a matrix. Our method is elementary as it relies upon the method of Schur complements, but it outperforms the one based on the Cassini ovals of Ostrovski and Brauer. Furthermore, it yields estimates that hold without major differences in the cases of both scalar and operator matrices. Several refinements of known results are obtained. |
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Keywords: | Estimates of the spectrum of matrices operator matrices of unbounded operators 47A10 15A42 |
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