Graphs and Hermitian matrices: exact interlacing

2006/09/20 by Bollobas, Bela, Nikiforov, Vladimir
#05C50 #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0609572

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.

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