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

Mathematics

Sugoog Shon¹  Yunlan Wei²  Yanpeng Zheng²  Zhaolin Jiang² 

[1] College of Information Technology, The University of Suwon, Hwaseong-si 445-743, Korea;School of Mathematics and Statistics, Linyi University, Linyi 276000, China;

关键词: determinant;    inverse;    Mersenne number;    periodic tridiagonal Toeplitz matrix;    Sherman-Morrison-Woodbury formula;   

DOI  :  10.3390/math7100893

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown