# Eigenvalues vs.matrix sparsity

For an n X n matrix whose entries are constrained to be in some [x,y], is the maximum absolute eigenvalue of the matrix a function of its sparsity?

Is there a closed-form expression that states this function?

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What is "sparsity" for you? A percentage of zero entries, or a precise sparsity pattern? –  Federico Poloni Sep 13 '12 at 20:37
A percentage of zero entries, for starters. –  Maniacka Sep 14 '12 at 19:33