We investigate the solvability of the matrix equation $ AX^{2} = B $ in which the multiplication is the semi-tensor product. Then compatible conditions on the matrices $ A $ and $ B $ 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.
Citation: Jin Wang, Jun-E Feng, Hua-Lin Huang. Solvability of the matrix equation $ AX^{2} = B $ with semi-tensor product[J]. Electronic Research Archive, 2021, 29(3): 2249-2267. doi: 10.3934/era.2020114
We investigate the solvability of the matrix equation $ AX^{2} = B $ in which the multiplication is the semi-tensor product. Then compatible conditions on the matrices $ A $ and $ B $ 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.
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