Matrices similar to centrosymmetric matrices

TL;DR

This paper establishes criteria for matrices to be similar to centrosymmetric matrices, demonstrating applications to Toeplitz matrices and matrix dilations, thus expanding understanding of matrix similarity transformations.

Contribution

It provides new conditions for matrix similarity to centrosymmetric matrices and explores their applications to specific matrix classes and dilations.

Findings

Certain 4x4 and 6x6 Toeplitz matrices are similar to centrosymmetric matrices.

Conditions are given for matrices to be similar to matrices with centrosymmetric principal submatrices.

The paper describes how matrices can be dilated to be similar to centrosymmetric matrices.

Abstract

In this paper we give conditions on a matrix which guarantee that it is similar to a centrosymmetric matrix. We use this conditions to show that some $4 \times 4$ and $6 \times 6$ Toeplitz matrices are similar to centrosymmetric matrices. Furthermore, we give conditions for a matrix to be similar to a matrix which has a centrosymmetric principal submatrix, and conditions under which a matrix can be dilated to a matrix similar to a centrosymmetric matrix.