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Determinants, Norms, and the Spread of Circulant Matrices with Tribonacci and Generalized Lucas Numbers

Author

Listed:
  • Juan Li
  • Zhaolin Jiang
  • Fuliang Lu

Abstract

Circulant matrices play an important role in solving ordinary and partial differential equations. In this paper, by using the inverse factorization of polynomial of degree n, the explicit determinants of circulant and left circulant matrix involving Tribonacci numbers or generalized Lucas numbers are expressed in terms of Tribonacci numbers and generalized Lucas numbers only. Furthermore, four kinds of norms and bounds for the spread of these matrices are given, respectively.

Suggested Citation

  • Juan Li & Zhaolin Jiang & Fuliang Lu, 2014. "Determinants, Norms, and the Spread of Circulant Matrices with Tribonacci and Generalized Lucas Numbers," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:381829
    DOI: 10.1155/2014/381829
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    References listed on IDEAS

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    1. Xiaoling Huang & Guodong Ye & Kwok-Wo Wong, 2013. "Chaotic Image Encryption Algorithm Based on Circulant Operation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. Bose, Arup & Mitra, Joydip, 2002. "Limiting spectral distribution of a special circulant," Statistics & Probability Letters, Elsevier, vol. 60(1), pages 111-120, November.
    3. Xiaoling Huang & Guodong Ye & Kwok-Wo Wong, 2013. "Chaotic Image Encryption Algorithm Based on Circulant Operation," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, July.
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    Cited by:

    1. Yanpeng Zheng & Sugoog Shon, 2015. "Exact Inverse Matrices of Fermat and Mersenne Circulant Matrix," Abstract and Applied Analysis, John Wiley & Sons, vol. 2015(1).
    2. Tingting Xu & Zhaolin Jiang & Ziwu Jiang, 2014. "Explicit Determinants of the RFPrLrR Circulant and RLPrFrL Circulant Matrices Involving Some Famous Numbers," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    3. Li Liu & Zhaolin Jiang, 2015. "Explicit Form of the Inverse Matrices of Tribonacci Circulant Type Matrices," Abstract and Applied Analysis, John Wiley & Sons, vol. 2015(1).
    4. Zhaolin Jiang & Hongxia Xin & Fuliang Lu, 2014. "Gaussian Fibonacci Circulant Type Matrices," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    5. Zhaolin Jiang & Yunlan Wei, 2015. "Skew Circulant Type Matrices Involving the Sum of Fibonacci and Lucas Numbers," Abstract and Applied Analysis, John Wiley & Sons, vol. 2015(1).

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