### Electronic Research Archive

2021, Issue 3: 2249-2267. doi: 10.3934/era.2020114
Special Issues

# Solvability of the matrix equation $AX^{2} = B$ with semi-tensor product

• Received: 01 May 2020 Revised: 01 August 2020 Published: 19 October 2020
• Primary: 15A06; Secondary: 15A03, 15A04

• 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

### Related Papers:

• 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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