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Research Article | Open Access

Four symmetric systems of the matrix equations with an application over the Hamilton quaternions

Long-Sheng Liu1, Shuo Zhang1, Hai-Xia Chang2( )
School of Mathematics and Physics, Anqing Normal University, Anqing 246011, China
School of Statistics and Mathematics, Shanghai Lixin University of Accounting and Finance, Shanghai 201209, China
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Abstract

In this paper, we established some necessary and sufficient conditions for the four symmetric systems to be consistent. Moreover, we derived the expressions of their general solutions when they were solvable. As an application, we investigated the solvability conditions of matrix equations involving η-Hermicity matrices. Finally, we presented an example to illustrate the main results of this paper.

Keywords

matrix equationquaternionMoore-Penroserankη-Hermitian matrix
CLC number: 15A03, 15A09, 15A24

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AIMS Mathematics
Volume 9 Issue 12,
December 2024
Pages 33662-33691
DOI: 10.3934/math.20241607

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Cite this article:
Liu L-S, Zhang S, Chang H-X. Four symmetric systems of the matrix equations with an application over the Hamilton quaternions. AIMS Mathematics, 2024, 9(12): 33662-33691. https://doi.org/10.3934/math.20241607

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Received: 04 August 2024
Revised: 30 October 2024
Accepted: 12 November 2024
Published: 15 December 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)