The paper deals with the third-order quaternion tensor equation. Based on the Qt multiplication operation, we derive solvability conditions and also get the general solution, the least-squares solution, the minimum-norm solution and the minimum-norm least-squares solution of the tensor equation $ \mathcal{A} \ast_{\mathbb{Q}} \mathcal{X} = \mathcal{B} $. Finally, two numerical examples are presented.
Citation: Xiaohan Li, Xin Liu, Jing Jiang, Jian Sun. Some solutions to a third-order quaternion tensor equation[J]. AIMS Mathematics, 2023, 8(11): 27725-27741. doi: 10.3934/math.20231419
The paper deals with the third-order quaternion tensor equation. Based on the Qt multiplication operation, we derive solvability conditions and also get the general solution, the least-squares solution, the minimum-norm solution and the minimum-norm least-squares solution of the tensor equation $ \mathcal{A} \ast_{\mathbb{Q}} \mathcal{X} = \mathcal{B} $. Finally, two numerical examples are presented.
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Xiaohan Li, Xin Liu, Jing Jiang, Jian Sun. Some solutions to a third-order quaternion tensor equation[J]. AIMS Mathematics, 2023, 8(11): 27725-27741. doi: 10.3934/math.20231419
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