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A Real Method for Solving Octonion Matrix Equation \(AXB=C\) Based on Semi-tensor Product of Matrices

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Abstract

In this paper, the octonion matrix equation \(AXB=C\) is studied based on semi-tensor product of matrices. Firstly, we propose the left real element representation and the right real element representation of octonion. Then we obtain the expression of the least squares Hermitian solution to the octonion matrix equation \(AXB=C\) by combining these representations with \(\mathcal {H}\)-representation of the special matrices. In addition, we also put forward the equivalent condition of existence and general expression of the Hermitian solution to the octonion matrix equation \(AXB=C.\) Finally, the validity and stability of our method is verified by numerical experiments.

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Authors and Affiliations

  1. Research Center of Semi-tensor Product of Matrices: Theory and Applications, College of Mathematical Sciences, Liaocheng University, Liaocheng, 252000, People’s Republic of China

    Xiaochen Liu, Ying Li, Wenxv Ding & Ruyu Tao

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  1. Xiaochen Liu
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  2. Ying Li
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  3. Wenxv Ding
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  4. Ruyu Tao
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Correspondence to Ying Li.

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Communicated by Hongbo Li.

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This work is supported by the National Natural Science Foundation of China [grant number 62176112] and the Natural Science Foundation of Shandong Province [grant number ZR2020MA053,ZR2022MA030]. and Discipline with Strong Characteristic of Liaocheng University Intelligent Science and Technology [grant number 319462208].

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Liu, X., Li, Y., Ding, W. et al. A Real Method for Solving Octonion Matrix Equation \(AXB=C\) Based on Semi-tensor Product of Matrices. Adv. Appl. Clifford Algebras 34, 12 (2024). https://doi.org/10.1007/s00006-024-01316-z

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