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

Yıl 2019, , 1 - 8, 30.04.2019

Emrullah Kırklar Fatih Yılmaz

https://doi.org/10.36753/mathenot.559232
Cited By: 2

Öz

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.

Anahtar Kelimeler

r-circulant determinant matrix inverse third order recurrence

Kaynakça

  • [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.

Yıl 2019, , 1 - 8, 30.04.2019

Emrullah Kırklar Fatih Yılmaz

https://doi.org/10.36753/mathenot.559232
Cited By: 2

Öz

Kaynakça

  • [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.
Toplam 11 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Articles
Yazarlar

Emrullah Kırklar

Fatih Yılmaz

Yayımlanma Tarihi 30 Nisan 2019
Gönderilme Tarihi 3 Ekim 2016
Yayımlandığı Sayı Yıl 2019

Kaynak Göster

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. Nisan 2019;7(1):1-8. doi:10.36753/mathenot.559232
Chicago Kırklar, Emrullah, ve Fatih Yılmaz. “A General Formula for Determinants and Inverses of R-Circulant Matrices With Third Order Recurrences”. Mathematical Sciences and Applications E-Notes 7, sy. 1 (Nisan 2019): 1-8. https://doi.org/10.36753/mathenot.559232.
EndNote Kırklar E, Yılmaz F (01 Nisan 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 ve F. Yılmaz, “A General Formula for Determinants and Inverses of r-circulant Matrices with Third Order Recurrences”, Math. Sci. Appl. E-Notes, c. 7, sy. 1, ss. 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 (Nisan 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 ve Fatih Yılmaz. “A General Formula for Determinants and Inverses of R-Circulant Matrices With Third Order Recurrences”. Mathematical Sciences and Applications E-Notes, c. 7, sy. 1, 2019, ss. 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.

Cited By

Some results on circulant matrices involving Fibonacci polynomials
AIMS Mathematics
https://doi.org/10.3934/math.2025425
Determinants of circulant matrices with Gaussian nickel Fibonacci numbers
Filomat
https://doi.org/10.2298/FIL2325683Y

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