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, …, xn} be an ordered set of distinct positive integers with x1 < x2 < … < xn (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

References

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  3. P. Haukkanen, J. Wang and J. Sillanpää,  On Smith’s determinant.  Linear Algebra Appl.  258  (1997), 251-269.
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  5. I. Korkee and P. Haukkanen, On meet and join matrices associated with incidence functions. Linear Algebra Appl.  372C (2003), 127-153.
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  8. N. Tuglu and D. Tasci, On the LCM-reciprocal GCD matrices. Far East J. Math. Sci. (FJMS) 6 (2002), no. 1, 89-94.

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Cite this paper

APA

Nalli, A., & Haukkanen, P. (2003). On the Hadamard product of GCD and LCM matrices associated with semi-multiplicative functions, Notes on Number Theory and Discrete Mathematics, 9(4), 90-98.

Chicago

Nalli, Ayse, and Pentti Haukkanen. “On the Hadamard Product of GCD and LCM Matrices Associated with Semi-multiplicative Functions.” Notes on Number Theory and Discrete Mathematics, 9, no. 4 (2003): 90-98.

MLA

Nalli, Ayse, and Pentti Haukkanen. “On the Hadamard Product of GCD and LCM Matrices Associated with Semi-multiplicative Functions.” Notes on Number Theory and Discrete Mathematics, 9.4 (2003): 90-98. Print.

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