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The eigenvalues of circulant matrices with generalized tetranacci numbers

Year 2021, , 417 - 423, 15.04.2021
https://doi.org/10.17714/gumusfenbil.830575

Abstract

Let the sequence 〖(T〗_n )_(n∈N) be the generalized tetranacci sequence. Define the n×n circulant matrix C(T) by c_ij={■(T_(j-i)&,j≥i@T_(n+j-i)&,j

Supporting Institution

AMASYA UNIVERSITY

Project Number

FMB-BAP 19-0419

References

  • Bahşi, M. (2015). On the norms of circulant matrices with the generalized Fibonacci and Lucas numbers. Turkic World Mathematical Society Journal of Pure and Applied Mathematics, 6(1), 84-92.
  • Bahsi, M. and Solak, S. (2014). On the norms of r-circulant matrices with the hyper-Fibonacci and Lucas numbers. Journal of Mathematical Inequalities, 8(4), 693-705.
  • Cauchy, A.L. (1829). Sur 1’bquation a l’aide de laquelle on determine les inegalities sqculaires des mouvements des planbtes, mineralogy and petrology. Exercices de Mathématiques, 4 = Oeuvres, (2)9, 174-95.
  • Davis, P. J. (1979). Circulant matrices. John Wiley and Sons: New York.
  • Feinberg, M. (1963). Fibonacci-Tribonacci. The Fibonacci Quarterly, 1(1), 71-74.
  • Hermite, C. (1855). Remarque sur un theoreme de M. Cauchy. Comptes Rendus de L’Académie des Sciences., 41 = Oeuvres 1, 459- 481.
  • Kızılateş, C. (2017). On the quadra Lucas-Jacobsthal numbers. Karaelmas Science and Engineering Journal, 7(2), 619-621.
  • Kızılateş, C. and Tuglu, N. (2016). On the bounds for the spectral norms of geometric circulant matrices. Journal of Inequalities and Applications, 2016(1), 1-15.
  • Kızılateş, C. and Tuglu, N. (2018). On the norms of geometric and symmetric geometric circulant matrices with the Tribonacci Number. Gazi University Journal of Science, 31(2), 555-567.
  • Kirkpatrick , T.B. (1977). Fibonacci sequences and additive triangles of higher order and degree. Fibonacci Quarterly, 15 (4), 319–322.
  • Kocer, E. G., Mansour, T. and Tuglu, N. (2007). Norms of circulant and semicirculant matrices with horadam's Numbers. Ars Combinatoria, 85, 353-359.
  • Özkoç, A. and Ardıyok, E. (2016). Circulant and negacyclic matrices via tetranacci numbers. Honam Mathematical Journal, 38(4), 725-738. https://doi.org/10.5831/HMJ.2016.38.4.725.
  • Shen, S. Q. and Cen, J. M. (2010). On the spectral norms of r-circulant matrices with the k-Fibonacci and k-Lucas numbers. International Journal of Contemporary Mathematical Sciences, 5(12), 569-578.
  • Solak, S. (2005). On the norms of circulant matrices with the Fibonacci and Lucas numbers. Applied Mathematics and Computation, 160(1), 125-132. https://doi.org/10.1016/j.amc.2003.08.126.
  • Spickerman, W.R. (1982). Binet's formula for the tribonacci sequence. The Fibonacci Quarterly, 20 (2), 118-120. Spickerman, W.R. and Joyner, R.N. (1984). Binet’s formula for the recursive sequence of order k. The Fibonacci Quarterly, 22 (4), 327–331.
  • Tascı, D. and Acar, H. (2017). Gaussian tetranacci numbers. Communications in Mathematics ans Applications, 8(3), 379-386 .
  • Tuglu, N. and Kızılateş, C. (2015a). On the norms of circulant and r-circulant matrices with the hyperharmonic Fibonacci numbers. Journal of Inequalities and Applications, 253(2015).
  • Tuglu, N. and Kızılateş, C. (2015b). On the norms of some special matrices with the harmonic Fibonacci numbers. Gazi University Journal of Science, 28(3), 497-501.
  • Tuglu, N., Kızılateş, C. and Kesim, S. (2015). On the harmonic and hyperharmonic Fibonacci numbers. Advances in Difference Equations, 2015(1), 1-12.
  • Waddill, M. E. (1992). The tetranacci sequence and generalizations. The Fibonacci Quarterly, 30(1), 9-20.
  • Yesil Baran, F. and Yetiş, T. (2019). On The norms of circulant matrices via generalized tetranacci numbers. Bilecik Seyh Edebali University Journal of Science, 6(2), 444-454. https://doi.org/10.35193/bseufbd.662239.
  • Zaveri M. N. and Patel, J. K. (2015). Binet’s formula for the tetranacci sequence. International Journal of Science and Research, 78-96.

Genelleştirilmiş tetranacci sayıları ile tanımlı circulant matrislerin özdeğerleri

Year 2021, , 417 - 423, 15.04.2021
https://doi.org/10.17714/gumusfenbil.830575

Abstract

〖(T〗_n )_(n∈N) genelleştirilmiş tetranacci dizisi ve C(T) , n×n tipinde i,j=1,2,… ,n için c_ij={■(T_(j-i)&,j≥i@T_(n+j-i)&,j

Project Number

FMB-BAP 19-0419

References

  • Bahşi, M. (2015). On the norms of circulant matrices with the generalized Fibonacci and Lucas numbers. Turkic World Mathematical Society Journal of Pure and Applied Mathematics, 6(1), 84-92.
  • Bahsi, M. and Solak, S. (2014). On the norms of r-circulant matrices with the hyper-Fibonacci and Lucas numbers. Journal of Mathematical Inequalities, 8(4), 693-705.
  • Cauchy, A.L. (1829). Sur 1’bquation a l’aide de laquelle on determine les inegalities sqculaires des mouvements des planbtes, mineralogy and petrology. Exercices de Mathématiques, 4 = Oeuvres, (2)9, 174-95.
  • Davis, P. J. (1979). Circulant matrices. John Wiley and Sons: New York.
  • Feinberg, M. (1963). Fibonacci-Tribonacci. The Fibonacci Quarterly, 1(1), 71-74.
  • Hermite, C. (1855). Remarque sur un theoreme de M. Cauchy. Comptes Rendus de L’Académie des Sciences., 41 = Oeuvres 1, 459- 481.
  • Kızılateş, C. (2017). On the quadra Lucas-Jacobsthal numbers. Karaelmas Science and Engineering Journal, 7(2), 619-621.
  • Kızılateş, C. and Tuglu, N. (2016). On the bounds for the spectral norms of geometric circulant matrices. Journal of Inequalities and Applications, 2016(1), 1-15.
  • Kızılateş, C. and Tuglu, N. (2018). On the norms of geometric and symmetric geometric circulant matrices with the Tribonacci Number. Gazi University Journal of Science, 31(2), 555-567.
  • Kirkpatrick , T.B. (1977). Fibonacci sequences and additive triangles of higher order and degree. Fibonacci Quarterly, 15 (4), 319–322.
  • Kocer, E. G., Mansour, T. and Tuglu, N. (2007). Norms of circulant and semicirculant matrices with horadam's Numbers. Ars Combinatoria, 85, 353-359.
  • Özkoç, A. and Ardıyok, E. (2016). Circulant and negacyclic matrices via tetranacci numbers. Honam Mathematical Journal, 38(4), 725-738. https://doi.org/10.5831/HMJ.2016.38.4.725.
  • Shen, S. Q. and Cen, J. M. (2010). On the spectral norms of r-circulant matrices with the k-Fibonacci and k-Lucas numbers. International Journal of Contemporary Mathematical Sciences, 5(12), 569-578.
  • Solak, S. (2005). On the norms of circulant matrices with the Fibonacci and Lucas numbers. Applied Mathematics and Computation, 160(1), 125-132. https://doi.org/10.1016/j.amc.2003.08.126.
  • Spickerman, W.R. (1982). Binet's formula for the tribonacci sequence. The Fibonacci Quarterly, 20 (2), 118-120. Spickerman, W.R. and Joyner, R.N. (1984). Binet’s formula for the recursive sequence of order k. The Fibonacci Quarterly, 22 (4), 327–331.
  • Tascı, D. and Acar, H. (2017). Gaussian tetranacci numbers. Communications in Mathematics ans Applications, 8(3), 379-386 .
  • Tuglu, N. and Kızılateş, C. (2015a). On the norms of circulant and r-circulant matrices with the hyperharmonic Fibonacci numbers. Journal of Inequalities and Applications, 253(2015).
  • Tuglu, N. and Kızılateş, C. (2015b). On the norms of some special matrices with the harmonic Fibonacci numbers. Gazi University Journal of Science, 28(3), 497-501.
  • Tuglu, N., Kızılateş, C. and Kesim, S. (2015). On the harmonic and hyperharmonic Fibonacci numbers. Advances in Difference Equations, 2015(1), 1-12.
  • Waddill, M. E. (1992). The tetranacci sequence and generalizations. The Fibonacci Quarterly, 30(1), 9-20.
  • Yesil Baran, F. and Yetiş, T. (2019). On The norms of circulant matrices via generalized tetranacci numbers. Bilecik Seyh Edebali University Journal of Science, 6(2), 444-454. https://doi.org/10.35193/bseufbd.662239.
  • Zaveri M. N. and Patel, J. K. (2015). Binet’s formula for the tetranacci sequence. International Journal of Science and Research, 78-96.
There are 22 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Fatma Yeşil Baran 0000-0001-8613-2706

Project Number FMB-BAP 19-0419
Publication Date April 15, 2021
Submission Date November 24, 2020
Acceptance Date February 28, 2021
Published in Issue Year 2021

Cite

APA Yeşil Baran, F. (2021). The eigenvalues of circulant matrices with generalized tetranacci numbers. Gümüşhane Üniversitesi Fen Bilimleri Dergisi, 11(2), 417-423. https://doi.org/10.17714/gumusfenbil.830575