On the Hadamard product of GCD and LCM matrices associated with semi-multiplicative functions

Ayse Nalli and Pentti Haukkanen
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 9, 2003, Number 4, Pages 90—98
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Authors and affiliations

Ayse Nalli
Department of Mathematics, Faculty of Science and Literature, University of Selcuk
42070 Campüs Konya, Turkey

Pentti Haukkanen
Department of Mathematics, Statistics and Philosophy,
FIN-33014 University of Tampere, Finland

Abstract

Let S = {x₁, x₂, …, x_n} be an ordered set of distinct positive integers with x₁ < x₂ < … < x_n (n > 1). We provide some properties for the n × n matrix (G)_f o [L]_f on S, where (G)_f denotes the n × n GCD matrix on S associated with f, [L]_f denotes the n × n LCM matrix on S associated with f and o denotes the Hadamard product.

Keywords

• Hadamard product
• GCD matrix
• LCM matrix
• Semi-multiplicative function

AMS Classification

• 11C20
• 11A05
• 15A36
• 11A25

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