English

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

Number Theory 2014-08-15 v1

Abstract

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

Keywords

Cite

@article{arxiv.1408.3113,
  title  = {On Bounds for the Smallest and the Largest Eigenvalues of GCD and LCM Matrices},
  author = {Ercan Altınışık and Şerife Büyükköse},
  journal= {arXiv preprint arXiv:1408.3113},
  year   = {2014}
}