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Explicit Form of the Inverse Matrices of Tribonacci Circulant Type Matrices

Author

Listed:
  • Li Liu
  • Zhaolin Jiang

Abstract

It is a hot topic that circulant type matrices are applied to networks engineering. The determinants and inverses of Tribonacci circulant type matrices are discussed in the paper. Firstly, Tribonacci circulant type matrices are defined. In addition, we show the invertibility of Tribonacci circulant matrix and present the determinant and the inverse matrix based on constructing the transformation matrices. By utilizing the relation between left circulant, g‐circulant matrices and circulant matrix, the invertibility of Tribonacci left circulant and Tribonacci g‐circulant matrices is also discussed. Finally, the determinants and inverse matrices of these matrices are given, respectively.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnlaaa:v:2015:y:2015:i:1:n:169726
    DOI: 10.1155/2015/169726
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    References listed on IDEAS

    as
    1. Xiaoyu Jiang & Kicheon Hong, 2014. "Exact Determinants of Some Special Circulant Matrices Involving Four Kinds of Famous Numbers," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    2. Zhaolin Jiang & Yanpeng Gong & Yun Gao, 2014. "Circulant Type Matrices with the Sum and Product of Fibonacci and Lucas Numbers," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-12, June.
    3. 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).
    4. Xiaoyu Jiang & Kicheon Hong, 2014. "Exact Determinants of Some Special Circulant Matrices Involving Four Kinds of Famous Numbers," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-12, June.
    5. Zhaolin Jiang & Yanpeng Gong & Yun Gao, 2014. "Circulant Type Matrices with the Sum and Product of Fibonacci and Lucas Numbers," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    6. 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, Hindawi, vol. 2014, pages 1-9, May.
    Full references (including those not matched with items on IDEAS)

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