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Tytuł artykułu

Determinants and inverses of circulant matrices with complex Fibonacci numbers

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let ℱn = circ (︀F*1 , F*2, . . . , F*n︀ be the n×n circulant matrix associated with complex Fibonacci numbers F*1, F*2, . . . , F*n. In the present paper we calculate the determinant of ℱn in terms of complex Fibonacci numbers. Furthermore, we show that ℱn is invertible and obtain the entries of the inverse of ℱn in terms of complex Fibonacci numbers.
Wydawca
Czasopismo
Rocznik
Tom
3
Numer
1
Opis fizyczny
Daty
otrzymano
2015-01-28
zaakceptowano
2015-04-15
online
2015-04-24
Twórcy
  • Gazi University, Faculty of Science, Department of Mathematics, Teknikokullar TR-
    06500, Ankara, Turkey
  • Harran University, Faculty of Arts and Sciences, Department of Mathematics, 63290, Şanlıurfa, Turkey
  • Gazi University, Faculty of Science, Department of Mathematics, Teknikokullar TR-
    06500, Ankara, Turkey
Bibliografia
  • [1] E. Altınışık, Ş. Büyükköse, Determinants of circulant matrices with some certain sequences, Gazi University Journal of Science28 (1) (2015), 59-63.
  • [2] D. Bozkurt, T. Y. Tam, Determinants and inverses of circulant matrices with Jacobsthal and Jacobsthal-Lucas numbers, App.Math. Comput. 219 (2012) 544-551.[WoS]
  • [3] D. Bozkurt, T. Y. Tam, Determinants and inverses of r−circulant matrices associated with a number sequence, Linear MultilinearAlgebra (2014) DOI:10.1080/03081087.2014.941291.[Crossref]
  • [4] P. J. Davis, Circulant Matrices, Wiley, New York, 1979.
  • [5] Z. Jiang, H Xin, F. Lu, Gaussian Fibonacci circulant type matrices, Abstr. Appl. Anal. 2014, Art. ID 592782, 10 pp.
  • [6] R. M. Gray, Toeplitz and Circulant Matrices: A review, Now Publishers Inc., Hanover, 2005.
  • [7] A. F. Horadam, Complex Fibonacci numbers and Fibonacci quaternions, Amer. Math. Monthly 70 (1963), 289–291.
  • [8] D. A. Lind, A circulant, Quart. 8 (1970) 449–455.
  • [9] S. Q. Shen, J. M. Cen, Y. Hao, On the determinants and inverses of circulant matrices with and Lucas numbers, App. Math.Comput. 217 (2011), 9790–9797.[WoS]
  • [10] S. Solak, On the norms of circulant matrices with with and Lucas numbers, App. Math. Comput. 160 (2005), 125–132.[WoS]
  • [11] M. Z. Spivey, Fibonacci identities via the determinant sum property, College Math. J. 37 (2006), 286–289.
  • [12] Y. Yazlık, N. Taşkara, On the inverse of circulantmatrix via generalized k-Horadam numbers, App.Math. Comput. 223 (2013),191–196.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_spma-2015-0008
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