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eigenvalues of matrices or operators

52 votes
8 answers
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Is there a fast way to check if a matrix has any small eigenvalues?

I have hundreds of millions of symmetric 0/1-matrices of moderate size (say 20x20 to 30x30) which (obviously) have real eigenvalues. … It seems though that this property is somewhat special because only a minuscule fraction of my hundreds of millions have no small eigenvalues. …