# Skew cyclic displacements and decompositions of inverse matrix for an innovative structure matrix

Volume 10, Issue 8, pp 4058--4070 Publication Date: August 06, 2017

### Authors

Xiaoyu Jiang - Department of Information and Telecommunications Engineering, The University of Suwon, Wau-ri, Bongdam-eup, Hwaseong-si, Gyeonggi-do, 445-743, Korea.
Kicheon Hong - Department of Information and Telecommunications Engineering, The University of Suwon, Wau-ri, Bongdam-eup, Hwaseong-si, Gyeonggi-do, 445-743, Korea.
Zunwei Fu - Department of Mathematics, The University of Suwon, Wau-ri, Bongdam-eup, Hwaseong-si, Gyeonggi-do, 445-743, Korea.

### Abstract

In this paper, we study mainly on a class of column upper-minus-lower (CUML) Toeplitz matrices without standard Toeplitz structure, which are  similar'' to the Toeplitz matrices. Their (-1,-1)-cyclic displacements coincide with cyclic displacement of some standard Toeplitz matrices. We obtain the formula on representation for the inverses of CUML Toeplitz matrices in the form of sums of products of (-1, 1)-circulants and (1, -1)-circulants factor by constructing the corresponding displacement of the matrices. In addition, based on the relation between CUML Toeplitz matrices and CUML Hankel matrices, the inverse formula of CUML Hankel matrices can also be obtained.

### Keywords

• CUML Toeplitz matrix
• CUML Hankel matrix
• skew cyclic displacement
• RSFPLR circulants
• RFMLR circulants
• decomposition
• inverse.

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