Ipek, Ahmet2024-09-182024-09-1820120898-1221https://doi.org/10.1016/j.camwa.2011.11.016https://hdl.handle.net/20.500.12483/10228Let S = {x(1), . . . , x(n)} be a set of n distinct positive integers. The n x n matrix having the greatest common divisor (x(i), x(j)) of x(i) and x(j) as its i, j-entry is called the greatest common divisor (GCD) matrix defined on S, denoted by ((x(i), x(j))), or abbreviated as (S). The n x n matrix (S-1) = (g(ij)), where g(ij) = 1/(x(i),x(j)) is called the reciprocal greatest common divisor (GCD) matrix on S. In this paper, we present upper bounds for the spectral condition numbers of the reciprocal GCD matrix (S-1) and the GCD matrix (S) defined on S = {1, 2, . . . , n}, with n >= 2, as a function of Euler's phi function and n. (C) 2011 Elsevier Ltd. All rights reserved.eninfo:eu-repo/semantics/openAccessGCD matricesMatrix normsEuler's phi functionArticle63364565110.1016/j.camwa.2011.11.0162-s2.0-84855818840Q1WOS:000300756500005Q1