A Note on the Norms of the GCD Matrix
Department of Mathematics, Selcuk Uliversity, 42031, Campus, Konya, Turkey
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Math. Comput. Appl. 2004, 9(2), 303-308; https://doi.org/10.3390/mca9020303
Published: 1 August 2004
Abstract
Let \(S=\{1,2,..., n\}\) be a set of positive integers. The \(n\times n\) 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 Hilbert-Smith GCD matrix is defined \((S)=\left[ \frac{(i,j)}{ij} \right]^{n}_{i,j=1}\)
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MDPI and ACS Style
Türkmen, R.; Bozkurt, D. A Note on the Norms of the GCD Matrix. Math. Comput. Appl. 2004, 9, 303-308. https://doi.org/10.3390/mca9020303
AMA Style
Türkmen R, Bozkurt D. A Note on the Norms of the GCD Matrix. Mathematical and Computational Applications. 2004; 9(2):303-308. https://doi.org/10.3390/mca9020303
Chicago/Turabian StyleTürkmen, Ramazan, and Durmuş Bozkurt. 2004. "A Note on the Norms of the GCD Matrix" Mathematical and Computational Applications 9, no. 2: 303-308. https://doi.org/10.3390/mca9020303
