@article{Wang2022, 
author = {Naiwen Wang},
title = {Solvability of the Sylvester equation  AX−XB=C under left semi-tensor product},
year = {2022},
journal = {Mathematical Modelling and Control},
volume = {2},
number = {2},
pages = {81-89},
keywords = {solvability, Sylvester matrix equation, left semi-tensor product, matrix-vector equation, necessary and sufficient condition},
url = {https://www.sciopen.com/article/10.3934/mmc.2022010},
doi = {10.3934/mmc.2022010},
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.}
}