The inverses and eigenpairs of tridiagonal Toeplitz matrices with perturbed rows

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.