A note on the norms of the GCD matrix

Abstract

Let S={1, 2,..., n} be a set of positive integers. The nXn matrix [S]=(i,j), where $S_{ij}=(X_i,X_j)$ the greatest common divisor of $x_i$ and $x_j$, is called the greatest common divisor GCD matrix on S. In this study, we have obtained some bounds of norms of this matrix. In addition, we have obtained upper bounds of norms of the almost Hubert-Smith GCD matrix is defined (S)=$[\frac{(i,j)}{ij}]^n_{i,j}$=1