| | | |

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

#### Emrullah Kırklar [1] , Fatih Yılmaz [2]

##### 36 72

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.
r-circulant, determinant, matrix inverse, third order recurrence
• [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.
Primary Language en Articles Author: Emrullah Kırklar (Primary Author) Author: Fatih Yılmaz Publication Date: April 30, 2019
 Bibtex @research article { mathenot559232, journal = {MSAEN}, issn = {}, eissn = {2147-6268}, address = {Murat TOSUN}, year = {2019}, volume = {7}, pages = {1 - 8}, doi = {}, title = {A General Formula for Determinants and Inverses of r-circulant Matrices with Third Order Recurrences}, key = {cite}, author = {Kırklar, Emrullah and Yılmaz, Fatih} } APA Kırklar, E , Yılmaz, F . (2019). A General Formula for Determinants and Inverses of r-circulant Matrices with Third Order Recurrences. MSAEN, 7 (1), 1-8. Retrieved from http://dergipark.org.tr/mathenot/issue/44921/559232 MLA Kırklar, E , Yılmaz, F . "A General Formula for Determinants and Inverses of r-circulant Matrices with Third Order Recurrences". MSAEN 7 (2019): 1-8 Chicago Kırklar, E , Yılmaz, F . "A General Formula for Determinants and Inverses of r-circulant Matrices with Third Order Recurrences". MSAEN 7 (2019): 1-8 RIS TY - JOUR T1 - A General Formula for Determinants and Inverses of r-circulant Matrices with Third Order Recurrences AU - Emrullah Kırklar , Fatih Yılmaz Y1 - 2019 PY - 2019 N1 - DO - T2 - MSAEN JF - Journal JO - JOR SP - 1 EP - 8 VL - 7 IS - 1 SN - -2147-6268 M3 - UR - Y2 - 2019 ER - EndNote %0 MSAEN A General Formula for Determinants and Inverses of r-circulant Matrices with Third Order Recurrences %A Emrullah Kırklar , Fatih Yılmaz %T A General Formula for Determinants and Inverses of r-circulant Matrices with Third Order Recurrences %D 2019 %J MSAEN %P -2147-6268 %V 7 %N 1 %R %U ISNAD Kırklar, Emrullah , Yılmaz, Fatih . "A General Formula for Determinants and Inverses of r-circulant Matrices with Third Order Recurrences". MSAEN 7 / 1 (April 2019): 1-8. AMA Kırklar E , Yılmaz F . A General Formula for Determinants and Inverses of r-circulant Matrices with Third Order Recurrences. MSAEN. 2019; 7(1): 1-8. Vancouver Kırklar E , Yılmaz F . A General Formula for Determinants and Inverses of r-circulant Matrices with Third Order Recurrences. MSAEN. 2019; 7(1): 8-1.