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Research Article | Open Access

Least squares solutions of matrix equation A X B = C under semi-tensor product

Department of Mathematics, Harbin Institute of Technology, Weihai 264209, China
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Abstract

This paper mainly studies the least-squares solutions of matrix equation A X B = C under a semi-tensor product. According to the definition of the semi-tensor product, the equation is transformed into an ordinary matrix equation. Then, the least-squares solutions of matrix-vector and matrix equations respectively investigated by applying the derivation of matrix operations. Finally, the specific form of the least-squares solutions is given.

Keywords

matrix equationssemi-tensor productleast squares solution

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Electronic Research Archive
Volume 32 Issue 5,
May 2024
Pages 2976-2993
DOI: 10.3934/era.2024136

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Cite this article:
Wang J. Least squares solutions of matrix equation A X B = C under semi-tensor product. Electronic Research Archive, 2024, 32(5): 2976-2993. https://doi.org/10.3934/era.2024136

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Received: 24 January 2024
Revised: 22 March 2024
Accepted: 12 April 2024
Published: 15 May 2024
©2024 the Author(s), licensee AIMS Press.

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