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On the Minimal Polynomials and the Inverses of Multilevel Scaled Factor Circulant Matrices

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  • Zhaolin Jiang

Abstract

Circulant matrices have important applications in solving various differential equations. The level‐k scaled factor circulant matrix over any field is introduced. Algorithms for finding the minimal polynomial of this kind of matrices over any field are presented by means of the algorithm for the Gröbner basis of the ideal in the polynomial ring. And two algorithms for finding the inverses of such matrices are also presented. Finally, an algorithm for computing the inverse of partitioned matrix with level‐k scaled factor circulant matrix blocks over any field is given by using the Schur complement, which can be realized by CoCoA 4.0, an algebraic system, over the field of rational numbers or the field of residue classes of modulo prime number.

Suggested Citation

  • Zhaolin Jiang, 2014. "On the Minimal Polynomials and the Inverses of Multilevel Scaled Factor Circulant Matrices," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:521643
    DOI: 10.1155/2014/521643
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    References listed on IDEAS

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    1. S. Georgiou & C. Koukouvinos, 2006. "Multi-level k-circulant Supersaturated Designs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 64(2), pages 209-220, October.
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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. Xiaoyu Jiang & Kicheon Hong, 2015. "Equalities and Inequalities for Norms of Block Imaginary Circulant Operator Matrices," Abstract and Applied Analysis, John Wiley & Sons, vol. 2015(1).
    3. 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).
    4. Zhaolin Jiang & Hongxia Xin & Fuliang Lu, 2014. "Gaussian Fibonacci Circulant Type Matrices," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    5. Wenai Xu & Zhaolin Jiang, 2015. "Norms and Spread of the Fibonacci and Lucas RSFMLR Circulant Matrices," Abstract and Applied Analysis, John Wiley & Sons, vol. 2015(1).

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