The explicit determinants, inverses and eigenpairs of periodic tridiagonal Toeplitz-like matrices with perturbed rows are presented in this paper. We derive the representation of the determinants and inverses in the form of products of Mersenne numbers and some initial values from matrix transformations, which reduces the computational complexity to a certain extent. Futhermore, we make some analysis about these basic quantities to illustrate our theoretical results.

中文翻译：

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具有扰动行的三对角Toeplitz矩阵的逆和本征对

给出了周期三对角Toeplitz样周期扰动行的显式行列式，逆和本征对。我们以矩阵转换的梅森数和一些初始值的乘积形式来获取行列式和逆的表示形式，从而在一定程度上降低了计算复杂度。此外，我们对这些基本量进行了一些分析，以说明我们的理论结果。