Determinants of Circulant Matrices with Some Certain Sequences

Yıl 2015, Cilt: 28 Sayı: 1, 59 - 63, 23.02.2015

Ercan Altınışık Şerife Büyükköse

Öz

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]. 

Anahtar Kelimeler

circulant matrix, determinant, Fibonacci sequence, Lucas sequence, tribonacci sequence

Determinants of Circulant Matrices with Some

Öz

Kaynakça

• 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
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• 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)