Dergiler / Gazi University Journal of Science / 2015 / Cilt: 28 - Sayı: 1

Determinants of Circulant Matrices with Some

Determinants of Circulant Matrices with Some Certain Sequences

Sayfa
59–63
Yayın Tarihi
2015-02-23
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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].

📌 3 Maddede Bu Makale

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Amaç & Hipotez:Let {a_k} be a sequence of real numbers defined by an mth order linear homogenous recurrence relation.
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Temel Bulgular & Veri:Let {a_k} be a sequence of real numbers defined by an mth order linear homogenous recurrence relation.
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Sonuç & Katkı: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].
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:circulant matrix · determinant · Fibonacci sequence

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].

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Bu Makaleye Atıf Yap

ALTINIŞIK, E., BÜYÜKKÖSE, Ş. (2015). Determinants of Circulant Matrices with Some. Gazi University Journal of Science, Cilt: 28 - Sayı: 1, 59–63. https://ajindex.com/articles/254736

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Kaynakça (9)

  1. Aldrovandi, R: Mathematical Physics: Stochastic, Circulant and Bell Matrices. World Scientific, New York (2001)
  2. 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)
  3. Bozkurt, D, Tam, TY: Determinants and inverses of circulant Jacobsthal-Lucas numbers. Appl. Math. Comput. 219, 544-551 (2012)
  4. Jacobsthal and Davis, PJ: Circulant Matrices. Wiley, New York (1979)
  5. Gray, RM: Toeplitz and Circulant Matrices: A review. Now Publishers Inc., Hanover (2005)
  6. Kra, I, Simanca, SR: On Circulant matrices: Notices of the AMS 59, 368-377 (2012)
  7. Lind, DA: A Fibonacci Circulant. Fibonacci Quart. 8, 449-455 (1970)
  8. 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)
  9. Solak, S: On the norms of circulant matrices with Fibonacci and Lucas numbers. Appl. Math. Comput. 160, 125-132 (2005)