Skew cyclic displacements and inversions of two innovative patterned Matrices

In this paper, we deal mainly with a class of column upper-plus-lower (CUPL) Toeplitz matrices without Toeplitz structure, which are “close” to the Toeplitz matrices in the sense that their (−1,1)-cyclic displacements coincide with cyclic displacement of some Toeplitz matrices. By constructing the corresponding displacement of the matrices, we derive the formulas on representation of the inverses of the CUPL Toeplitz matrices in the form of sums of products of factor (1, 1)-circulants and (−1,−1)-circulants. Furthermore, through the relation between the CUPL Toeplitz matrices and the CUPL Hankel matrices, the inverses of the CUPL Hankel matrices can be obtained as well.