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

2014/08/13 by Ercan Altınışık, Altınışık, Ercan, Şerife Büyükköse +1
Computer Science · Mathematics · Physics and Astronomy · #05C88 #05C89 #Advanced Mathematical Theories and Applications #Coding theory and cryptography #FOS: Mathematics #Matrix Theory and Algorithms #Number Theory (math.NT) #math.NT #msc:05C88 #msc:05C89

paper · pdf · doi:10.48550/arxiv.1408.3113

arxiv created 2014/08/13 · openalex publication_date 2014/08/13 · arxiv updated 2014/08/15 · openalex created_date 2022/08/13 · openalex updated_date 2026/07/28

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,…,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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