Solvability of the matrix equation $ AX^{2} = B $ with semi-tensor product
Jin Wang, Jun‐e Feng, Hua-Lin Huang · Electronic Research Archive · 2020
We investigate the solvability of the matrix equation \begin{document}$ AX^{2} = B $\end{document} in which the multiplication is the semi-tensor product. Then compatible conditions on the matrices \begin{document}$ A $\end{document} and \begin{document}$ B $\end{document} are established in each case and necessary and sufficient condition for the solvability is discussed. In addition, concrete methods of solving the equation are provided.