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Research Article | Open Access

Solving reduced biquaternion matrices equation ∑ i = 1 k A i X B i = C with special structure based on semi-tensor product of matrices

Wenxv Ding1,2, Ying Li1,2( ), Anli Wei1,2, Zhihong Liu1,2
College of Mathematical Sciences, Liaocheng University, Liaocheng 252000, China
Research Center of Semi-tensor Product of Matrices: Theory and Applications, Liaocheng 252000, China
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Abstract

In this paper, we propose a real vector representation of reduced quaternion matrix and study its properties. By using this real vector representation, Moore-Penrose inverse, and semi-tensor product of matrices, we study some kinds of solutions of reduced biquaternion matrix equation (1.1). Several numerical examples show that the proposed algorithm is feasible at last.

Keywords

semi-tensor product of matricesreduced biquaternionmatrix equationreal vector representation
CLC number: 15A06

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AIMS Mathematics
Volume 7 Issue 3,
March 2022
Pages 3258-3276
DOI: 10.3934/math.2022181

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Cite this article:
Ding W, Li Y, Wei A, et al. Solving reduced biquaternion matrices equation ∑ i = 1 k A i X B i = C with special structure based on semi-tensor product of matrices. AIMS Mathematics, 2022, 7(3): 3258-3276. https://doi.org/10.3934/math.2022181

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Received: 18 September 2021
Accepted: 22 November 2021
Published: 15 March 2021
©2022 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)