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Research Article | Open Access

Solvability of the Sylvester equation AX−XB=C under left semi-tensor product

School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, China
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Abstract

This paper investigates the solvability of the Sylvester matrix equation AX−XB=C with respect to left semi-tensor product. Firstly, we discuss the matrix-vector equation AX−XB=C under semi-tensor product. A necessary and sufficient condition for the solvability of the matrix-vector equation and specific solving methods are studied and given. Based on this, the solvability of the matrix equation AX−XB=C under left semi-tensor product is discussed. Finally, several examples are presented to illustrate the efficiency of the results.

Keywords

Sylvester matrix equationleft semi-tensor productsolvabilitymatrix-vector equationnecessary and sufficient condition

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Mathematical Modelling and Control
Volume 2 Issue 2,
June 2022
Pages 81-89
DOI: 10.3934/mmc.2022010

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Cite this article:
Wang N. Solvability of the Sylvester equation AX−XB=C under left semi-tensor product. Mathematical Modelling and Control, 2022, 2(2): 81-89. https://doi.org/10.3934/mmc.2022010

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Received: 31 March 2022
Revised: 08 April 2022
Accepted: 20 April 2022
Published: 15 June 2022
©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)