Graphs and Hermitian matrices: exact interlacing
classification
🧮 math.CO
math.AC
keywords
largestmatrixboundconditionseigenvalueeigenvaluesequalityexact
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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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