On the determinants of some kinds of circulant-type matrices with generalized number sequences

• Autorzy: Emrullah Kirklar , Fatih Yilmaz
• Języki publikacji: EN

Abstrakty

EN

Recently, determinant computation of circulant type matrices with well-known number sequences has been studied, extensively. This study provides the determinants of the RFMLR, RLMFL, RFPrLrR and RLPrFrL circulant matrices with generalized number sequences of second order.

• Wydawca: De Gruyter Open
• Czasopismo: Special Matrices
• Rocznik: 2015
• Tom: 3
• Numer: 1

Daty

otrzymano

2015-08-05

zaakceptowano

2015-10-03

online

2015-10-16

Twórcy

autor

Emrullah Kirklar

• Department of Mathematics, Polatlı Art and Science Faculty, Gazi
  University, 06900, Ankara, Turkey

autor

Fatih Yilmaz

• Department of Mathematics, Polatlı Art and Science Faculty, Gazi
  University, 06900, Ankara, Turkey

Bibliografia

• [1] S.-Q. Shen, J.M. Cen, Y. Hao, On the determinants and inverses of circulant matrices with Fibonacci and Lucas numbers,Appl. Math. Comput. 217 (2011), no.23, 9790-9797.
• [2] D. Bozkurt, T.Y. Tam, Determinants and inverses of circulant matrices with Jacobsthal and Jacobsthal-Lucas numbers, Appl.Math. Comput. 219 (2012), no.2, 544-551.
• [3] D. Bozkurt, On the determinants and inverses of circulantmatriceswith a general number sequence, arXiv:1202.1068, 2012.
• [4] A. F. Horadam, Basic properties of a certain generalized sequence of numbers, Fibonacci Quart. 3.3 (1965): 161-176.
• [5] N. Shen, Z. Jiang, J. Li, On explicit determinants of the RFMLR and RLMFL circulant matrices involving certain famous numbers,WSEAS Trans. Math., 2013:42-53.
• [6] Z. Jiang, N. Shen, J. Li, Determinants of the RFMLR circulantmatriceswith Perrin, Padovan, Tribonacci, and generalized Lucasnumbers, J. Appl. Math., 2014, Article ID 585438, pp. 1-11.
• [7] Z. P. Tian, Fast algorithms for solving the inverse problem of AX = b in four different families of patternedmatrices, Far EastJ. Appl. Math.52, 2011, pp. 1–12.
• [8] D. Chillag, Regular representations of semisimple algebras, separable field extensions, group characters, generalized circulants,and generalized cyclic codes, Linear Algebra Appl.218, 1995, pp. 147–183.
• [9] P.J. Davis, Circulant Matrices, Wiley, NewYork, 1979.
• [10] Z. L. Jiang and Z. X. Zhou, Circulant Matrices, Chengdu Technology University Publishing Company, Chengdu, 1999.
• [11] T. Xu, Z. Jiang, Z Jiang, Explicit determinants of the RFPrLrR circulant and RLPrFrL circulant matrices involving some famousnumbers, Abstr. Appl. Anal., 2014, Article ID 647030, 9 p.
• [12] Y. Gao, Z. Jiang, Y. Gong, On determinants and inverses of skew circulant and skew circulant matrices with Fibonacci andLucas numbers, WSEAS Trans. Math., 2013, 12, 472-481.
• [13] X. Jiang, K. Hong, Exact determinants of some special circulant matrices involving four kinds of famous numbers, Abstr.Appl. Anal., 2014, Article ID 273680, 12 p.
• [14] Z. Jiang, J. Li, N. Shen, On the explicit determinants and singularities of r-circulant and left r-circulant matrices with somefamous numbers, WSEAS Trans. Math.,2013, 12, 341-351.

Identyfikatory

DOI

10.1515/spma-2015-0023