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Volume 10, Number 1, 2020, Pages 178-191                                                                DOI:10.11948/20190105
On inverses and eigenpairs of periodic tridiagonal Toeplitz matrices with perturbed corners
Yunlan Wei,Xiaoyu Jiang,Zhaolin Jiang,Sugoog Shon
Keywords:Determinant, inverse, eigenpair, periodic tridiagonal Toeplitz matrix.
Abstract:
      In this paper, we derive explicit determinants, inverses and eigenpairs of periodic tridiagonal Toeplitz matrices with perturbed corners of Type I. The Mersenne numbers play an important role in these explicit formulas derived. Our main approaches include clever uses of the Schur complement and matrix decomposition with the Sherman-Morrison-Woodbury formula. Besides, the properties of Type II matrix can be also obtained, which benefits from the relation between Type I and II matrices. Lastly, we give three algorithms for these basic quantities and analyze them to illustrate our theoretical results.
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