호남수학학술지 (Honam Mathematical Journal)

  • 제38권4호
  • /
  • Pages.725-738
  • /
  • 2016
  • /
  • 1225-293X(pISSN)
  • /
  • 2288-6176(eISSN)
호남수학회 (The Honam Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

CIRCULANT AND NEGACYCLIC MATRICES VIA TETRANACCI NUMBERS

  • Ozkoc, Arzu (Duzce University, Faculty of Science and Art, Department of Mathematics Konuralp) ;
  • Ardiyok, Elif (Duzce University, Faculty of Science and Art, Department of Mathematics Konuralp)
  • 투고 : 2016.04.26
  • 심사 : 2016.11.09
  • 발행 : 2016.12.25
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, the explicit determinants of the circulant and negacyclic matrix involving Tetranacci sequence $M_n$ and Companion-Tetranacci sequence $K_n$ are expressed by using only Tetranacci sequence $M_n$ and Companion-Tetranacci sequence $K_n$. Also euclidean norms and spectral norms of circulant and negacyclic matrices have been obtained.

키워드

참고문헌

  1. P. J. Davis,Circulant Matrices(John Wiley &Sons, New York, 1979).
  2. R. A. Horn. C.R. Matrix Analysis (Cambridge University Press, 1985).
  3. H. Karner, J.C. Schneid and W. Ueberhuber. Spectral decomposition of real circulant matrices, Linear Algebra and Its Applications 367, (2003), 301-311. https://doi.org/10.1016/S0024-3795(02)00664-X
  4. E.G. Kocer, Circulant, Negacyclic and Semicirculant Matrices with the Modified Pell, Jacobsthal-Lucas numbers. Hacettepe Journal of Mathematics and Statistics 36(2)(2007), 133-142.
  5. T. Koshy. Fibonacci and Lucas Numbers with Applications. John Wiley and Sons, 2001.
  6. P. Ribenboim. My Numbers, My Friends, Popular Lectures on Number Theory, Springer-Verlag, New York, Inc. 2000.
  7. S.Q. Shen, J.M. Cen, On the determinants and inverses of circulant matrices with the Fibonacci and Lucas numbers, Applied Mathematics and Computation, 217, (2011), 9790-9797. https://doi.org/10.1016/j.amc.2011.04.072
  8. W. R. Spickerman & R. N. Joyner. Binet's Formula for the Recursive Sequence of Order k. Fibonacci Quarterly 22.4 (1984), 327-31.
  9. M.E. Waddill. The Tetranacci Sequence and Generalizations. Fibonacci Quarterly 30.1(1992), 9-20.
  10. Z. Yanpeng, S. Shon, S. Lee and D. Oh. Determinant of the Generalized Lucas RSFMLR Circulant Matrices in Communication. International Conference on Information Computing and Applications. Springer-Verlag Berlin, Heidelberg, Part I, CCIS 391, pp. (2013), 72-81.
  11. Z. Yanpeng, S. Shon. Exact Inverse Matrices of Fermat and Mersenne Circulant Matrix. Abstract and Applied Analysis. Vol. (2015), Article ID 760823, 10 pages.
  12. Z. Yanpeng, S. Shon. Exact Determinants and Inverses of Generalized Lucas Skew Circulant Type Matrices. Applied Mathematics and Computation. 270(2015), 105-113. https://doi.org/10.1016/j.amc.2015.08.021