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Determinants of Circulant Matrices with Some Certain Sequences

Year 2015, Volume: 28 Issue: 1, 59 - 63, 23.02.2015

Abstract

Let {a_k} be a sequence of real numbers defined by an mth order linear homogenous recurrence relation. In this paper we obtain a determinant formula for the circulant matrix A=circ(a_1,a_2,...,a_n), providing a generalization of determinantal results in papers of Bozkurt [2], Bozkurt and Tam [3], and Shen, et al. [8]. 

References

  • Aldrovandi, R: Mathematical Physics: Stochastic, Circulant and Bell Matrices. World Scientific, New York (2001)
  • Bozkurt, D, Tam, TY: Determinants and inverses of r-circulant matrices associated with a number sequence. Linear and Multilinear Algebra. DOI:10.1080/03081087.2014.941291 (2014)
  • Bozkurt, D, Tam, TY: Determinants and inverses of circulant Jacobsthal-Lucas numbers. Appl. Math. Comput. 219, 544-551 (2012) Jacobsthal and
  • Davis, PJ: Circulant Matrices. Wiley, New York (1979)
  • Gray, RM: Toeplitz and Circulant Matrices: A review. Now Publishers Inc., Hanover (2005)
  • Kra, I, Simanca, SR: On Circulant matrices: Notices of the AMS 59, 368-377 (2012)
  • Lind, DA: A Fibonacci Circulant. Fibonacci Quart. 8, 449-455 (1970)
  • Shen, SQ, Cen JM, Hao, Y: On the determinants and inverses of circulant matrices with Fibonacci and Lucas numbers. Appl. Math. Comput. 217, 9790-9797 (2011)
  • Solak, S: On the norms of circulant matrices with Fibonacci and Lucas numbers. Appl. Math. Comput. 160, 125-132 (2005)

Determinants of Circulant Matrices with Some

Year 2015, Volume: 28 Issue: 1, 59 - 63, 23.02.2015

Abstract

References

  • Aldrovandi, R: Mathematical Physics: Stochastic, Circulant and Bell Matrices. World Scientific, New York (2001)
  • Bozkurt, D, Tam, TY: Determinants and inverses of r-circulant matrices associated with a number sequence. Linear and Multilinear Algebra. DOI:10.1080/03081087.2014.941291 (2014)
  • Bozkurt, D, Tam, TY: Determinants and inverses of circulant Jacobsthal-Lucas numbers. Appl. Math. Comput. 219, 544-551 (2012) Jacobsthal and
  • Davis, PJ: Circulant Matrices. Wiley, New York (1979)
  • Gray, RM: Toeplitz and Circulant Matrices: A review. Now Publishers Inc., Hanover (2005)
  • Kra, I, Simanca, SR: On Circulant matrices: Notices of the AMS 59, 368-377 (2012)
  • Lind, DA: A Fibonacci Circulant. Fibonacci Quart. 8, 449-455 (1970)
  • Shen, SQ, Cen JM, Hao, Y: On the determinants and inverses of circulant matrices with Fibonacci and Lucas numbers. Appl. Math. Comput. 217, 9790-9797 (2011)
  • Solak, S: On the norms of circulant matrices with Fibonacci and Lucas numbers. Appl. Math. Comput. 160, 125-132 (2005)
There are 9 citations in total.

Details

Primary Language English
Journal Section Mathematics
Authors

Ercan Altınışık

Şerife Büyükköse This is me

Publication Date February 23, 2015
Published in Issue Year 2015 Volume: 28 Issue: 1

Cite

APA Altınışık, E., & Büyükköse, Ş. (2015). Determinants of Circulant Matrices with Some Certain Sequences. Gazi University Journal of Science, 28(1), 59-63.
AMA Altınışık E, Büyükköse Ş. Determinants of Circulant Matrices with Some Certain Sequences. Gazi University Journal of Science. February 2015;28(1):59-63.
Chicago Altınışık, Ercan, and Şerife Büyükköse. “Determinants of Circulant Matrices With Some Certain Sequences”. Gazi University Journal of Science 28, no. 1 (February 2015): 59-63.
EndNote Altınışık E, Büyükköse Ş (February 1, 2015) Determinants of Circulant Matrices with Some Certain Sequences. Gazi University Journal of Science 28 1 59–63.
IEEE E. Altınışık and Ş. Büyükköse, “Determinants of Circulant Matrices with Some Certain Sequences”, Gazi University Journal of Science, vol. 28, no. 1, pp. 59–63, 2015.
ISNAD Altınışık, Ercan - Büyükköse, Şerife. “Determinants of Circulant Matrices With Some Certain Sequences”. Gazi University Journal of Science 28/1 (February 2015), 59-63.
JAMA Altınışık E, Büyükköse Ş. Determinants of Circulant Matrices with Some Certain Sequences. Gazi University Journal of Science. 2015;28:59–63.
MLA Altınışık, Ercan and Şerife Büyükköse. “Determinants of Circulant Matrices With Some Certain Sequences”. Gazi University Journal of Science, vol. 28, no. 1, 2015, pp. 59-63.
Vancouver Altınışık E, Büyükköse Ş. Determinants of Circulant Matrices with Some Certain Sequences. Gazi University Journal of Science. 2015;28(1):59-63.