ON THE EIGENVALUES OF CERTAIN NUMBER-THEORETIC MATRICES

Abstract

In this paper we study the structure and give bounds for the eigen

values of the n×n matrix, whose ij entry is (i, j) α[i, j] β, where α, β ∈ R,

(i, j) is the greatest common divisor of i and j and [i, j] is the least com

mon multiple of i and j. Currently, only O-estimates for the greatest

eigenvalue of this matrix can be found in the literature, and the asymp

totic behaviour of the greatest and smallest eigenvalues is known in case

when α = β.