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

Yunlan Wei, Yanpeng Zheng, Zhaolin Jiang and Sugoog Shon
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Yunlan Wei: School of Mathematics and Statistics, Linyi University, Linyi 276000, China
Yanpeng Zheng: School of Mathematics and Statistics, Linyi University, Linyi 276000, China
Zhaolin Jiang: School of Mathematics and Statistics, Linyi University, Linyi 276000, China
Sugoog Shon: College of Information Technology, The University of Suwon, Hwaseong-si 445-743, Korea

Mathematics, 2019, vol. 7, issue 10, 1-11

Abstract: 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.

Keywords: determinant; inverse; Mersenne number; periodic tridiagonal Toeplitz matrix; Sherman-Morrison-Woodbury formula (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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