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VanderLaan Circulant Type Matrices

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  • Hongyan Pan
  • Zhaolin Jiang

Abstract

Circulant matrices have become a satisfactory tools in control methods for modern complex systems. In the paper, VanderLaan circulant type matrices are presented, which include VanderLaan circulant, left circulant, and g‐circulant matrices. The nonsingularity of these special matrices is discussed by the surprising properties of VanderLaan numbers. The exact determinants of VanderLaan circulant type matrices are given by structuring transformation matrices, determinants of well‐known tridiagonal matrices, and tridiagonal‐like matrices. The explicit inverse matrices of these special matrices are obtained by structuring transformation matrices, inverses of known tridiagonal matrices, and quasi‐tridiagonal matrices. Three kinds of norms and lower bound for the spread of VanderLaan circulant and left circulant matrix are given separately. And we gain the spectral norm of VanderLaan g‐circulant matrix.

Suggested Citation

  • Hongyan Pan & Zhaolin Jiang, 2015. "VanderLaan Circulant Type Matrices," Abstract and Applied Analysis, John Wiley & Sons, vol. 2015(1).
    • Handle: RePEc:wly:jnlaaa:v:2015:y:2015:i:1:n:329329
    DOI: 10.1155/2015/329329
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    References listed on IDEAS

    as
    1. Zhaolin Jiang & Jinjiang Yao & Fuliang Lu, 2014. "On Skew Circulant Type Matrices Involving Any Continuous Fibonacci Numbers," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-10, June.
    2. 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).
    3. 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, Hindawi, vol. 2014, pages 1-10, April.
    4. 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.
    5. Shen Yin & Guang Wang & Xu Yang, 2014. "Robust PLS approach for KPI-related prediction and diagnosis against outliers and missing data," International Journal of Systems Science, Taylor & Francis Journals, vol. 45(7), pages 1375-1382, July.
    6. Zhaolin Jiang & Dan Li, 2014. "The Invertibility, Explicit Determinants, and Inverses of Circulant and Left Circulant and -Circulant Matrices Involving Any Continuous Fibonacci and Lucas Numbers," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-14, July.
    7. Zhaolin Jiang & Dan Li, 2014. "The Invertibility, Explicit Determinants, and Inverses of Circulant and Left Circulant and g‐Circulant Matrices Involving Any Continuous Fibonacci and Lucas Numbers," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    8. 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).
    9. 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).
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