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Research Article | Open Access

An η-Hermitian solution to a two-sided matrix equation and a system of matrix equations over the skew-field of quaternions

Mahmoud S. Mehany1,2( ), Faizah D. Alanazi3
Department of Mathematics, Faculty of Education, Ain Shams University, Cairo, 11566, Egypt
School of Science and Technology, NOVA University, Lisbon, Cairo Campus, New Cairo, 2024, Egypt
Department of Mathematics, College of Science, Northern Border University, Arar, Saudi Arabia
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Abstract

This study investigated η -Hermitian solutions to a two-sided matrix equation and a system of matrix equations over the skew-field of quaternions. We employed solvability conditions to identify the general solution for this system. This method deduces the Moore-Penrose inverse, and the rank equalities for the system's coefficients. We utilized these strategies to develop an algorithm that can compute general solutions. We also used these algorithms in numerical instances to verify the theoretical results.

Keywords

linear matrix equationsMATLAB softwarenonstandard involutiongeneralized inversesmatrix rank
CLC number: 15A05, 15A09, 15A36, 15A63, 68W30

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AIMS Mathematics
Volume 10 Issue 4,
April 2025
Pages 7684-7705
DOI: 10.3934/math.2025352

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Cite this article:
Mehany MS, Alanazi FD. An η-Hermitian solution to a two-sided matrix equation and a system of matrix equations over the skew-field of quaternions. AIMS Mathematics, 2025, 10(4): 7684-7705. https://doi.org/10.3934/math.2025352

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Received: 15 January 2025
Revised: 11 March 2025
Accepted: 17 March 2025
Published: 15 April 2025
©2025 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)