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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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