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Research Article | Open Access

Minimum-norm least-squares solutions of generalized Sylvester-type quaternion matrix equation with bi-Hermitian and skew bi-Hermitian constraints

Sinem Şimşek1, Tuğba Demirkol2, Yıldız Kulaç2, Halim Özdemir2( )
Department of Mathematics, Faculty of Arts and Sciences, Kırklareli University, Kırklareli 39100, Turkey
Department of Mathematics, Faculty of Science, Sakarya University, Sakarya 54050, Turkey
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Abstract

This paper investigated minimum-norm least-squares solutions to the quaternion matrix equation K X L + M Y N = O, where the unknown matrices X and Y were subject to bi-Hermitian or skew bi-Hermitian constraints. Building on the derived theoretical results, an explicit numerical algorithm was proposed. Moreover, several numerical examples were presented to validate the accuracy of these results.

Keywords

quaternion matrix equationsreal matrix representationminimum norm least-squares solutionsbi-Hermitian solutionsskew bi-Hermitian solutions
CLC number: 15A06, 15A09, 15A24, 15B33, 15B57

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AIMS Mathematics
Volume 11 Issue 4,
April 2026
Pages 9210-9227
DOI: 10.3934/math.2026380

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Şimşek S, Demirkol T, Kulaç Y, et al. Minimum-norm least-squares solutions of generalized Sylvester-type quaternion matrix equation with bi-Hermitian and skew bi-Hermitian constraints. AIMS Mathematics, 2026, 11(4): 9210-9227. https://doi.org/10.3934/math.2026380

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Received: 30 December 2025
Revised: 11 March 2026
Accepted: 23 March 2026
Published: 03 April 2026
©2026 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)