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Journals / Mathematical and Computational Applications / 2004 / Cilt: 9 - Sayı: 1

The GCD-reciprocal LCM matrices on GCD-closed sets

AYŞE NALLI
Dursun TAŞCI
Pages
101–106
DOI
—
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

We have obtained formula for the determinant and the inverse of the GCD-Reciprocal LCM matrix defined on gcd-closed sets.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:We have given a structure theorem for the GCD-Reciprocal LCM matrix and then we have calculated the value of the determinant of the GCD-Reciprocal LCM matrix.
📊
Key Findings & Data:We have given a structure theorem for the GCD-Reciprocal LCM matrix and then we have calculated the value of the determinant of the GCD-Reciprocal LCM matrix.
💡
Conclusion & Impact:We have obtained formula for the determinant and the inverse of the GCD-Reciprocal LCM matrix defined on gcd-closed sets.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

We have given a structure theorem for the GCD-Reciprocal LCM matrix and then we have calculated the value of the determinant of the GCD-Reciprocal LCM matrix. We have obtained formula for the determinant and the inverse of the GCD-Reciprocal LCM matrix defined on gcd-closed sets.

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Cite This Article

NALLI, A., TAŞCI, D. (2004). The GCD-reciprocal LCM matrices on GCD-closed sets. Mathematical and Computational Applications, Cilt: 9 - Sayı: 1, 101–106. https://ajindex.com/articles/280482

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References (1)

  1. H. J. S. Smith, On the value of a certain arithmetical determinant, Proc. London Math. Soc. 7,208-212, 1875/76. 2.R. Sivaramakrishnan, Classical Theory of Arithmetic Functions, Monographs Textbooks Pure Appl. Math., 126, Marcel Dekker, New York, 1989. 3.S. Beşlin and S. Ligh, Another Generalization of Smith's Determinant, Bull. Australian Math. Soc. 40(3), 413-415, 1989. 4.S. Beşlin and S. Ligh, Greatest common divisor matrices, Linear Algebra Appl. 118, 69-76, 1989. 5.S.Beşlin, Reciprocal GCD matrices and LCM matrices, Fibonacci Quart. 29, 271- 274,1991.