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

Year 2019, , 1 - 8, 30.04.2019
https://doi.org/10.36753/mathenot.559232

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.

References

  • [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] 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] 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] 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] 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] Davis, P.J., Circulant Matrices, Wiley, NewYork, 1979.
  • [7] Jiang, Z.L. and Zhou, Z.X., Circulant Matrices, Chengdu Technology University Publishing Company, Chengdu, 1999.
  • [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] 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] 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.
  • [11] Bozkurt, D. and Yılmaz, F., On the determinants and inverses of circulant matrices with Pell and Pell-Lucas numbers, http://arxiv.org/pdf/1201.6061v1.pdf, 2012.
Year 2019, , 1 - 8, 30.04.2019
https://doi.org/10.36753/mathenot.559232

Abstract

References

  • [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] 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] 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] 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] 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] Davis, P.J., Circulant Matrices, Wiley, NewYork, 1979.
  • [7] Jiang, Z.L. and Zhou, Z.X., Circulant Matrices, Chengdu Technology University Publishing Company, Chengdu, 1999.
  • [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] 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] 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.
  • [11] Bozkurt, D. and Yılmaz, F., On the determinants and inverses of circulant matrices with Pell and Pell-Lucas numbers, http://arxiv.org/pdf/1201.6061v1.pdf, 2012.
There are 11 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Emrullah Kırklar This is me

Fatih Yılmaz This is me

Publication Date April 30, 2019
Submission Date October 3, 2016
Published in Issue Year 2019

Cite

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 Kırklar E, Yılmaz F. A General Formula for Determinants and Inverses of r-circulant Matrices with Third Order Recurrences. Math. Sci. Appl. E-Notes. April 2019;7(1):1-8. doi:10.36753/mathenot.559232
Chicago 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 7, no. 1 (April 2019): 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 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, 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 2019), 1-8. https://doi.org/10.36753/mathenot.559232.
JAMA 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, 2019, pp. 1-8, doi:10.36753/mathenot.559232.
Vancouver 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.

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