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Graphs and Hermitian matrices: Exact interlacing |
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| Authors: | Béla Bollobás Vladimir Nikiforov |
| Institution: | a Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, USA b Department of Pure Mathematics & Mathematical Statistics, University of Cambridge Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WB, UK |
| Abstract: | We prove conditions for equality between the extreme eigenvalues of a matrix and its quotient. In particular, we give a lower bound on the largest singular value of a matrix and generalize a result of Finck and Grohmann about the largest eigenvalue of a graph. |
| Keywords: | Extreme eigenvalues Tight interlacing Graph Laplacian Singular values Nonnegative matrix |
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