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Determinants and inverses of weighted Loeplitz and weighted Foeplitz matrices and their applications in data encryption

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Abstract

In this paper, we investigate the analytical determinants and inverses of \(n\times n\) weighted Loeplitz and weighted Foeplitz matrices. We introduce the \(n\times n\) weighted Loeplitz and weighted Foeplitz matrices and derive the analytical determinants and inverses of them by constructing the transformation matrices. Specifically, we can use the nth, \((n+1)\)st and \((n+2)\)th Fibonacci numbers to express the analytical inverse of the \(n\times n\) weighted Loeplitz matrix which is sparse. We also present the analytical determiants and inverses of the \(n\times n\) weighted Lankel and weighted Fankel matrices. Finally, we give two application examples of the main results in data and image encryption.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Linyi University, Linyi, 276000, China

    Qingyan Meng & Zhaolin Jiang

  2. School of Automation and Electrical Engineering, Linyi University, Linyi, 276000, China

    Yanpeng Zheng

Authors
  1. Qingyan Meng
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  2. Yanpeng Zheng
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  3. Zhaolin Jiang
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Correspondence to Yanpeng Zheng or Zhaolin Jiang.

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The research was supported by the National Natural Science Foundation of China (No. 12001257 ), the Natural Science Foundation of Shandong Province ( No.ZR2020QA035) and the PhD Research Foundation of Linyi University ( No. LYDX2018BS067)

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Meng, Q., Zheng, Y. & Jiang, Z. Determinants and inverses of weighted Loeplitz and weighted Foeplitz matrices and their applications in data encryption. J. Appl. Math. Comput. 68, 3999–4015 (2022). https://doi.org/10.1007/s12190-022-01700-7

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  • DOI: https://doi.org/10.1007/s12190-022-01700-7

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