The eigenvalues of circulant matrices with generalized tetranacci numbers

Yıl 2021, , 417 - 423, 15.04.2021

Fatma Yeşil Baran

https://doi.org/10.17714/gumusfenbil.830575

Öz

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

Anahtar Kelimeler

Determinant, Eigenvalue, Tetranacci numbers

Destekleyen Kurum

AMASYA UNIVERSITY

Proje Numarası

FMB-BAP 19-0419

Genelleştirilmiş tetranacci sayıları ile tanımlı circulant matrislerin özdeğerleri

Öz

〖(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

Anahtar Kelimeler

Determinant, Özdeğer, Tetranacci sayıları

Proje Numarası

FMB-BAP 19-0419

Kaynakça

• 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.