Bela Bollobas, Vladimir Nikiforov
Published 2006-09-20, updated 2006-09-21Version 2
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.
Graphs and Hermitian matrices: discrepancy and singular values
Inertia indices and eigenvalue inequalities for Hermitian matrices
Lower bound for the rank of rigidity matrix of 4-valent graphs under various connectivity assumptions
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