A note on the norms of the GCD matrix

Key Findings & Data: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.

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Conclusion & Impact: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

🔬Design:Research Article

📍Scope:Comprehensive Sample

⚙️Variables:Domain Parameters

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

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Cite This Article

TÜRKMEN, R., BOZKURT, D. (2004). A note on the norms of the GCD matrix. Mathematical and Computational Applications, Cilt: 9 - Sayı: 2, 303–308. https://ajindex.com/articles/280347

References (1)

Roger A. Horn and Charles R. Johnson, Topics in Matrix Analysis, Cambridge University Press, 1991. 2.Ercan Altınışık, unpublished PhD. thesis, Selçuk University, 1991. 3.Beşlin Scott and Ligh Steve, Greatest common divisor matrices, Linear Algebra and Its Applications, 118, 69-76, 1989. 4.T. Ando, Roger A. Horn and Charles R. Johnson, the singuler values of a Hadamard Product: A basic inequality, Linear and Multilinear Algebra, 21, 345-365, 1987. 5.Tom M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, New York, 1976.