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On Bounds for the Smallest and the Largest Eigenvalues of GCD and LCM Matrices

Published 13 Aug 2014 in math.NT | (1408.3113v1)

Abstract: In this paper, we study the eigenvalues of the GCD matrix $(S_n)$ and the LCM matrix $[S_n]$ defined on $S_n={1,2,\ldots,n}$. We present upper and lower bounds for the smallest and the largest eigenvalues of $(S_n)$ and $[S_n]$ in terms of particular arithmetical functions.

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