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The Determinants, Inverses, Norm, and Spread of Skew Circulant Type Matrices Involving Any Continuous Lucas Numbers

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  • Jin-jiang Yao
  • Zhao-lin Jiang

Abstract

We consider the skew circulant and skew left circulant matrices with any continuous Lucas numbers. Firstly, we discuss the invertibility of the skew circulant matrices and present the determinant and the inverse matrices by constructing the transformation matrices. Furthermore, the invertibility of the skew left circulant matrices is also discussed. We obtain the determinants and the inverse matrices of the skew left circulant matrices by utilizing the relationship between skew left circulant matrices and skew circulant matrix, respectively. Finally, the four kinds of norms and bounds for the spread of these matrices are given, respectively.

Suggested Citation

  • Jin-jiang Yao & Zhao-lin Jiang, 2014. "The Determinants, Inverses, Norm, and Spread of Skew Circulant Type Matrices Involving Any Continuous Lucas Numbers," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:239693
    DOI: 10.1155/2014/239693
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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. 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. Zhaolin Jiang & Jinjiang Yao & Fuliang Lu, 2014. "On Skew Circulant Type Matrices Involving Any Continuous Fibonacci Numbers," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    2. Hongyan Pan & Zhaolin Jiang, 2015. "VanderLaan Circulant Type Matrices," Abstract and Applied Analysis, John Wiley & Sons, vol. 2015(1).
    3. Yanpeng Zheng & Sugoog Shon, 2015. "Exact Inverse Matrices of Fermat and Mersenne Circulant Matrix," Abstract and Applied Analysis, John Wiley & Sons, vol. 2015(1).

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