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Research Article | Open Access

Constrainted least squares solution of Sylvester equation

Wenxv Ding, Ying Li( ), Dong Wang, AnLi Wei
Research Center of Semi-tensor Product of Matrices: Theory and Applications, College of Mathematical Sciences, Liaocheng University, Liaocheng, 252000, China
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Abstract

In this paper, we study several constrainted least squares solutions of quaternion Sylvester matrix equation. We first propose a real vector representation of quaternion matrix and study its properties. By using this real vector representation, semi-tensor product of matrices, swap matrix and Moore-Penrose inverse, we derive compatible conditions and the expressions of several constrainted least squares solutions of quaternion Sylvester equation.

Keywords

quaternion matrix equationleast squares solutionsemi-tensor product of matricesreal vector representation(anti)η-Hermitian matrix

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Mathematical Modelling and Control
Volume 1 Issue 2,
June 2021
Pages 112-120
DOI: 10.3934/mmc.2021009

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Cite this article:
Ding W, Li Y, Wang D, et al. Constrainted least squares solution of Sylvester equation. Mathematical Modelling and Control, 2021, 1(2): 112-120. https://doi.org/10.3934/mmc.2021009

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Received: 18 March 2021
Accepted: 20 June 2021
Published: 15 June 2021
©2021 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)