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

Ercan Altınışık, Şerife Büyükköse

In this paper, we study the eigenvalues of the GCD matrix $(S_n)$ and the LCM matrix $[S_n]$ defined on $S_n=\{1,2,\dots ,n\}$. We present upper and lower bounds for the smallest a…