Research Article

A General Formula for Determinants and Inverses of r-circulant Matrices with Third Order Recurrences

Volume: 7 Number: 1 April 30, 2019
Emrullah Kırklar *, Fatih Yılmaz
EN

A General Formula for Determinants and Inverses of r-circulant Matrices with Third Order Recurrences

Abstract

This note provides formula for determinant and inverse of r-circulant matrices with general sequences of
third order. In other words, the study combines many papers in the literature.

Keywords

r-circulant,determinant,matrix inverse,third order recurrence

References

  1. [1] Shen, S. and Cen, J., On the bounds for the norms of r-circulant matrices with the Fibonacci and Lucas numbers, Applied Mathematics and Computation, 216 (2010) 2891–2897.
  2. [2] Shen, S.Q., Cen, J.M. and Hao, Y., On the determinants and inverses of circulant matrices with Fibonacci and Lucas numbers, Appl. Math. Comput. 217 (2011), no.23, 9790-9797.
  3. [3] Bozkurt, D. and Tam, T.Y., Determinants and Inverses of circulant matrices with Jacobsthal and Jacobsthal-Lucas numbers, Appl. Math. Comput. 219 (2012), no.2, 544-551.
  4. [4] Bozkurt, D. and Tam, T.Y., Determinants and inverses of r-circulant matrices associated with a number sequence, Linear and Multilinear Algebra, 2015, Vol. 63, No. 10, 2079–2088.
  5. [5] Yazlik, Y. and Taskara, N., On the inverse of circulant matrix via generalized k-Horadam numbers, Applied Mathematics and Computation, 223 (2013) 191–196.
  6. [6] Davis, P.J., Circulant Matrices, Wiley, NewYork, 1979.
  7. [7] Jiang, Z.L. and Zhou, Z.X., Circulant Matrices, Chengdu Technology University Publishing Company, Chengdu, 1999.
  8. [8] Liu, L. and Jiang, Z., Explicit Form of the Inverse Matrices of Tribonacci Circulant Type Matrices, Abstract and Applied Analysis, 2015, Article ID 169726.
  9. [9] Bozkurt, D., Da Fonseca, C.M. and Yılmaz, F., The determinants of circulant and skew-circulant matrices with Tribonacci numbers, Mathematical Sciences And Applications E-Notes, Volume 2 No. 2 pp. 67–75 (2014).
  10. [10] Zhao, G., The improved nonsingularity on the r-circulant matrices in signal processing, International Conference on Computer Technology and Development - ICCTD 2009, Kota Kinabalu, 564-567.
APA
Kırklar, E., & Yılmaz, F. (2019). A General Formula for Determinants and Inverses of r-circulant Matrices with Third Order Recurrences. Mathematical Sciences and Applications E-Notes, 7(1), 1-8. https://doi.org/10.36753/mathenot.559232
AMA
1.Kırklar E, Yılmaz F. A General Formula for Determinants and Inverses of r-circulant Matrices with Third Order Recurrences. Math. Sci. Appl. E-Notes. 2019;7(1):1-8. doi:10.36753/mathenot.559232
Chicago
Kırklar, Emrullah, and Fatih Yılmaz. 2019. “A General Formula for Determinants and Inverses of R-Circulant Matrices With Third Order Recurrences”. Mathematical Sciences and Applications E-Notes 7 (1): 1-8. https://doi.org/10.36753/mathenot.559232.
EndNote
Kırklar E, Yılmaz F (April 1, 2019) A General Formula for Determinants and Inverses of r-circulant Matrices with Third Order Recurrences. Mathematical Sciences and Applications E-Notes 7 1 1–8.
IEEE
[1]E. Kırklar and F. Yılmaz, “A General Formula for Determinants and Inverses of r-circulant Matrices with Third Order Recurrences”, Math. Sci. Appl. E-Notes, vol. 7, no. 1, pp. 1–8, Apr. 2019, doi: 10.36753/mathenot.559232.
ISNAD
Kırklar, Emrullah - Yılmaz, Fatih. “A General Formula for Determinants and Inverses of R-Circulant Matrices With Third Order Recurrences”. Mathematical Sciences and Applications E-Notes 7/1 (April 1, 2019): 1-8. https://doi.org/10.36753/mathenot.559232.
JAMA
1.Kırklar E, Yılmaz F. A General Formula for Determinants and Inverses of r-circulant Matrices with Third Order Recurrences. Math. Sci. Appl. E-Notes. 2019;7:1–8.
MLA
Kırklar, Emrullah, and Fatih Yılmaz. “A General Formula for Determinants and Inverses of R-Circulant Matrices With Third Order Recurrences”. Mathematical Sciences and Applications E-Notes, vol. 7, no. 1, Apr. 2019, pp. 1-8, doi:10.36753/mathenot.559232.
Vancouver
1.Emrullah Kırklar, Fatih Yılmaz. A General Formula for Determinants and Inverses of r-circulant Matrices with Third Order Recurrences. Math. Sci. Appl. E-Notes. 2019 Apr. 1;7(1):1-8. doi:10.36753/mathenot.559232