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

Year 2019, , 1 - 8, 30.04.2019

Emrullah Kırklar Fatih Yılmaz

https://doi.org/10.36753/mathenot.559232

Cited By: 1

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] 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.