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Explicit Expression for Arbitrary Positive Integer Powers of Special Sparse Matrices

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  • Mohammad Beiranvand
  • Mojtaba Ghasemi Kamalvand

Abstract

Sparse matrices appear frequently in mathematical models. In this paper, we firstly present a general expression for the entries of the r th (r ∈ ℕ) power of a certain n‐square sparse matrix, in terms of the Chebyshev polynomials of the second kind. Secondly, we present a method for integer positive powers of the skew matrix corresponding to these sparse matrices. This method will be inspiring to calculate the positive integer powers of the similar matrices. Finally, we present some examples to illustrate our results. Also, we give maple 18 procedures in order to verify our calculations.

Suggested Citation

  • Mohammad Beiranvand & Mojtaba Ghasemi Kamalvand, 2022. "Explicit Expression for Arbitrary Positive Integer Powers of Special Sparse Matrices," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:1076545
    DOI: 10.1155/2022/1076545
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    1. Mohammad Beiranvand & Mojtaba Ghasemi Kamalvand, 2020. "Explicit Expression for Arbitrary Positive Powers of Special Tridiagonal Matrices," Journal of Applied Mathematics, John Wiley & Sons, vol. 2020(1).
    2. Mohammad Beiranvand & Mojtaba Ghasemi Kamalvand, 2020. "Explicit Expression for Arbitrary Positive Powers of Special Tridiagonal Matrices," Journal of Applied Mathematics, Hindawi, vol. 2020, pages 1-5, September.
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