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Article

A Study of Determinants and Inverses for Periodic Tridiagonal Toeplitz Matrices with Perturbed Corners Involving Mersenne Numbers

1
School of Mathematics and Statistics, Linyi University, Linyi 276000, China
2
College of Information Technology, The University of Suwon, Hwaseong-si 445-743, Korea
3
School of Automation and Electrical Engineering, Linyi University, Linyi 276000, China
*
Authors to whom correspondence should be addressed.
Mathematics 2019, 7(10), 893; https://doi.org/10.3390/math7100893
Received: 5 July 2019 / Revised: 18 September 2019 / Accepted: 20 September 2019 / Published: 24 September 2019
(This article belongs to the Special Issue Mathematical Analysis and Analytic Number Theory 2019)
In this paper, we study periodic tridiagonal Toeplitz matrices with perturbed corners. By using some matrix transformations, the Schur complement and matrix decompositions techniques, as well as the Sherman-Morrison-Woodbury formula, we derive explicit determinants and inverses of these matrices. One feature of these formulas is the connection with the famous Mersenne numbers. We also propose two algorithms to illustrate our formulas. View Full-Text
Keywords: determinant; inverse; Mersenne number; periodic tridiagonal Toeplitz matrix; Sherman-Morrison-Woodbury formula determinant; inverse; Mersenne number; periodic tridiagonal Toeplitz matrix; Sherman-Morrison-Woodbury formula
MDPI and ACS Style

Wei, Y.; Zheng, Y.; Jiang, Z.; Shon, S. A Study of Determinants and Inverses for Periodic Tridiagonal Toeplitz Matrices with Perturbed Corners Involving Mersenne Numbers. Mathematics 2019, 7, 893. https://doi.org/10.3390/math7100893

AMA Style

Wei Y, Zheng Y, Jiang Z, Shon S. A Study of Determinants and Inverses for Periodic Tridiagonal Toeplitz Matrices with Perturbed Corners Involving Mersenne Numbers. Mathematics. 2019; 7(10):893. https://doi.org/10.3390/math7100893

Chicago/Turabian Style

Wei, Yunlan, Yanpeng Zheng, Zhaolin Jiang, and Sugoog Shon. 2019. "A Study of Determinants and Inverses for Periodic Tridiagonal Toeplitz Matrices with Perturbed Corners Involving Mersenne Numbers" Mathematics 7, no. 10: 893. https://doi.org/10.3390/math7100893

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