Determinants and inverses of circulant matrices with complex Fibonacci numbers

Ercan Altınışık; N. Feyza Yalçın; Şerife Büyükköse

Special Matrices (2015)

  • Volume: 3, Issue: 1, page 82-90, electronic only
  • ISSN: 2300-7451

Abstract

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Let ℱn = circ (︀F*1 , F*2, . . . , F*n︀ be the n×n circulant matrix associated with complex Fibonacci numbers F*1, F*2, . . . , F*n. In the present paper we calculate the determinant of ℱn in terms of complex Fibonacci numbers. Furthermore, we show that ℱn is invertible and obtain the entries of the inverse of ℱn in terms of complex Fibonacci numbers.

How to cite

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Ercan Altınışık, N. Feyza Yalçın, and Şerife Büyükköse. "Determinants and inverses of circulant matrices with complex Fibonacci numbers." Special Matrices 3.1 (2015): 82-90, electronic only. <http://eudml.org/doc/270970>.

@article{ErcanAltınışık2015,
abstract = {Let ℱn = circ (︀F*1 , F*2, . . . , F*n︀ be the n×n circulant matrix associated with complex Fibonacci numbers F*1, F*2, . . . , F*n. In the present paper we calculate the determinant of ℱn in terms of complex Fibonacci numbers. Furthermore, we show that ℱn is invertible and obtain the entries of the inverse of ℱn in terms of complex Fibonacci numbers.},
author = {Ercan Altınışık, N. Feyza Yalçın, Şerife Büyükköse},
journal = {Special Matrices},
keywords = {Circulant matrix; determinant; complex Fibonacci sequence; Fibonacci sequence; circulant matrix; complex Fibonacci numbers; inverse},
language = {eng},
number = {1},
pages = {82-90, electronic only},
title = {Determinants and inverses of circulant matrices with complex Fibonacci numbers},
url = {http://eudml.org/doc/270970},
volume = {3},
year = {2015},
}

TY - JOUR
AU - Ercan Altınışık
AU - N. Feyza Yalçın
AU - Şerife Büyükköse
TI - Determinants and inverses of circulant matrices with complex Fibonacci numbers
JO - Special Matrices
PY - 2015
VL - 3
IS - 1
SP - 82
EP - 90, electronic only
AB - Let ℱn = circ (︀F*1 , F*2, . . . , F*n︀ be the n×n circulant matrix associated with complex Fibonacci numbers F*1, F*2, . . . , F*n. In the present paper we calculate the determinant of ℱn in terms of complex Fibonacci numbers. Furthermore, we show that ℱn is invertible and obtain the entries of the inverse of ℱn in terms of complex Fibonacci numbers.
LA - eng
KW - Circulant matrix; determinant; complex Fibonacci sequence; Fibonacci sequence; circulant matrix; complex Fibonacci numbers; inverse
UR - http://eudml.org/doc/270970
ER -

References

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  1. [1] E. Altınışık, Ş. Büyükköse, Determinants of circulant matrices with some certain sequences, Gazi University Journal of Science 28 (1) (2015), 59-63. Zbl1307.15016
  2. [2] D. Bozkurt, T. Y. Tam, Determinants and inverses of circulant matrices with Jacobsthal and Jacobsthal-Lucas numbers, App. Math. Comput. 219 (2012) 544-551. [WoS] Zbl1302.15005
  3. [3] D. Bozkurt, T. Y. Tam, Determinants and inverses of r−circulant matrices associated with a number sequence, Linear Multilinear Algebra (2014) DOI:10.1080/03081087.2014.941291. [Crossref] Zbl06519818
  4. [4] P. J. Davis, Circulant Matrices, Wiley, New York, 1979. Zbl0418.15017
  5. [5] Z. Jiang, H Xin, F. Lu, Gaussian Fibonacci circulant type matrices, Abstr. Appl. Anal. 2014, Art. ID 592782, 10 pp. 
  6. [6] R. M. Gray, Toeplitz and Circulant Matrices: A review, Now Publishers Inc., Hanover, 2005. Zbl1143.15305
  7. [7] A. F. Horadam, Complex Fibonacci numbers and Fibonacci quaternions, Amer. Math. Monthly 70 (1963), 289–291. Zbl0122.29402
  8. [8] D. A. Lind, A circulant, Quart. 8 (1970) 449–455. 
  9. [9] S. Q. Shen, J. M. Cen, Y. Hao, On the determinants and inverses of circulant matrices with and Lucas numbers, App. Math. Comput. 217 (2011), 9790–9797. [WoS] Zbl1222.15010
  10. [10] S. Solak, On the norms of circulant matrices with with and Lucas numbers, App. Math. Comput. 160 (2005), 125–132. [WoS] Zbl1066.15029
  11. [11] M. Z. Spivey, Fibonacci identities via the determinant sum property, College Math. J. 37 (2006), 286–289. 
  12. [12] Y. Yazlık, N. Taşkara, On the inverse of circulantmatrix via generalized k-Horadam numbers, App.Math. Comput. 223 (2013), 191–196. Zbl1334.15076

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