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Math. Comput. Appl. 2004, 9(2), 303-308; doi:10.3390/mca9020303

A Note on the Norms of the GCD Matrix

Department of Mathematics, Selcuk Uliversity, 42031, Campus, Konya, Turkey
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Published: 1 August 2004
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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 \((S)=\left[ \frac{(i,j)}{ij} \right]^{n}_{i,j=1}\)
Keywords: Matrix Norm; Unitarily Invariant Norm; GCD matrix; Hadamard Product; Singular Values; Positive Definite Matrix Norm; Unitarily Invariant Norm; GCD matrix; Hadamard Product; Singular Values; Positive Definite
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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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.

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