Mathematics Faculty Articles

Document Type

Article

Publication Date

9-24-2019

Publication Title

Special Matrices

Keywords

Multilevel Toeplitz matrix, Unitary similarity, Complex symmetric matrices

ISSN

2300-7451

Volume

7

Issue/No.

1

First Page

114

Last Page

126

Abstract

Chien, Liu, Nakazato and Tam proved that all n × n classical Toeplitz matrices (one-level Toeplitz matrices) are unitarily similar to complex symmetric matrices via two types of unitary matrices and the type of the unitary matrices only depends on the parity of n. In this paper we extend their result to multilevel Toeplitz matrices that any multilevel Toeplitz matrix is unitarily similar to a complex symmetric matrix. We provide a method to construct the unitary matrices that uniformly turn any multilevel Toeplitz matrix to a complex symmetric matrix by taking tensor products of these two types of unitary matrices for one-level Toeplitz matrices according to the parity of each level of the multilevel Toeplitz matrices. In addition, we introduce a class of complex symmetric matrices that are unitarily similar to some p-level Toeplitz matrices.

Comments

©2019 Lei Cao and Selcuk Koyuncu, published by De Gruyter. This work is licensed under the Creative Commons Attribution alone 4.0 License.

Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

ORCID ID

0000-0001-7613-7191

ResearcherID

G-7341-2019

DOI

10.1515/spma-2019-0011

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