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arXiv · 1408.3113

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

Ercan Altınışık·Şerife Büyükköse
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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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Ercan Altınışık, Şerife Büyükköse. 2014-08-13. On Bounds for the Smallest and the Largest Eigenvalues of GCD and LCM Matrices. https://arxiv.org/abs/1408.3113

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