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Article
A Note on Multilevel Toeplitz Matrices
Special Matrices
  • Lei Cao, Nova Southeastern University
  • Selcuk Koyuncu, University of North Georgia
Document Type
Article
Publication Date
9-24-2019
Keywords
  • Multilevel Toeplitz matrix,
  • Unitary similarity,
  • Complex symmetric matrices
Disciplines
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
ORCID ID
0000-0001-7613-7191
ResearcherID
G-7341-2019
DOI
10.1515/spma-2019-0011
Citation Information
Lei Cao and Selcuk Koyuncu. "A Note on Multilevel Toeplitz Matrices" Special Matrices Vol. 7 Iss. 1 (2019) p. 114 - 126 ISSN: 2300-7451
Available at: http://works.bepress.com/lei-cao/8/