Journal of the
Korean Mathematical Society JKMS

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J. Korean Math. Soc. 2022; 59(5): 997-1013

Online first article July 29, 2022      Printed September 1, 2022

https://doi.org/10.4134/JKMS.j220108

Copyright © The Korean Mathematical Society.

Matrices similar to centrosymmetric matrices

Benjamín A. Itzá-Ortiz, Rubén A. Martínez-Avendaño

Universidad Aut\'onoma del Estado de Hidalgo; Instituto Tecnol\'ogico Aut\'onomo de M\'exico

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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.

Keywords: Centrosymmetric matrices, determinants, similarity, matrix equations

MSC numbers: 15B99, 15A15, 15A24

Supported by: The second author's research is partially supported by the Asociaci\'on Mexicana de Cultura A.C.

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