GCED reciprocal LCEM matrices

Zahid Raza and Seemal Abdul Waheed
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 21, 2015, Number 1, Pages 79—85
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Authors and affiliations

Zahid Raza
Department of Mathematics
National University of Computer & Emerging Sciences
B-Block, Faisal Town, Lahore, Pakistan

Seemal Abdul Waheed
Department of Mathematics
National University of Computer & Emerging Sciences
B-Block, Faisal Town, Lahore, Pakistan

Abstract

We have given structure theorems for a greatest common exponential divisor (GCED) and reciprocal least common exponential multiple (LCEM) matrix and calculated their determinants. The inverses and determinants of GCED and reciprocal LCEM matrices on exponential divisor closed sets have been determined.

Keywords

  • GCED matrix
  • Reciprocal LCEM matrix
  • Exponential divisor
  • Exponential divisor closed set

AMS Classification

  • 15B36
  • 15A36

References

  1. Altinisk, E., D. Tasci. (2002) On a generalization of LCM matrix, Common. fac. Sci. Univ. Ank. Series A, 51(2), 37–46.
  2. Beslin, S. J., S. Ligh. (1989) Greatest common divisor matrices, Linear Algebra Appl., 118, 69–76.
  3. Beslin, S. J. (1991) Reciprocal GCD matrices and LCM matrices, Fibonacci Quart. 29, 271–274.
  4. Feng, W., S. Hong, J. Zhao. (2009) Divisibilty of power LCM matrices by power GCD matrices on gcd-closed sets, Discrete Math., 309, 2627–2639.
  5. Nalli, A., D. Tasci. (2004) The GCD-reciprocal LCM matrices on gcd closed sets, Math. Comput. Appl., 9, 101–106.
  6. Rajarama Bhat, B. V. (1991) On greatest common divisor matrices and their applications, Linear Algebra Appl., 158, 77–97.
  7. Raza, Z., S.Waheed. GCED and Reciprocal GCED matrices to appear in Hacettepe Journal of Mathematics and Statistics.
  8. Raza, Z., S. A. Waheed. (2012) LCEM and reciprocal GCED matrices, Int. J. Pure and Applied Mathematics, 80(5), 647–655.
  9. Smith, H. J. (1875) On the value of a certain arithmetical determinant, Proc. London Math Soc., 7, 208–212.
  10. Sandor, J., B. Crstici. (2005) Handbook of Number Theory II, Springer.
  11. Subrarao, M. V. (1972) On some arithmetical convolutions: The theory of arithmetic functions, Lecture Notes in Mathematics, Springer.
  12. Tuglu, N., D. Tasci. (2002) On the LCUM-reciprocal GCUD matrices, Comptes rendus de l’ Academie bulgare des Sciences, 55(12), 17–21.
  13. Toth, L. (2009) On certain arithmetical functions involving exponential divisors, arXiv:math/0610274v2[math.NT].

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Cite this paper

APA

Raza, Z., & Waheed, S. A. (2015). GCED reciprocal LCEM matrices. Notes on Number Theory and Discrete Mathematics, 21(1), 79-85.

Chicago

Raza, Zahid, and Seemal Abdul Waheed. “GCED Reciprocal LCEM Matrices.” Notes on Number Theory and Discrete Mathematics 21, no. 1 (2015): 79-85.

MLA

Raza, Zahid, and Seemal Abdul Waheed. “GCED Reciprocal LCEM Matrices.” Notes on Number Theory and Discrete Mathematics 21.1 (2015): 79-85. Print.

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