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Several kinds of special least squares solutions to quaternion matrix equation \(AXB=C\)

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Abstract

In this paper, we apply the semi-tensor product of matrices and the real vector representation of quaternion matrix to solve quaternion matrix equations for the first time. We derive the expressions of the least squares Hermitian, Persymmetric and Bisymmetric solution for the quaternion matrix equation \(AXB=C\), respectively. Furthermore, we also put forward the equivalent conditions of existence and general expression of the Hermitian, Persymmetric and Bisymmetric solution to the quaternion matrix equation \(AXB=C\), respectively. Finally, the validity of our method is verified by numerical experiments with different dimensions.

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Authors and Affiliations

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

    Dong Wang, Ying Li & Wenxv Ding

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  1. Dong Wang
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  2. Ying Li
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  3. Wenxv Ding
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Correspondence to Ying Li.

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Supported by the Natural Science Foundation of Shandong under grant ZR2020MA053.

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Wang, D., Li, Y. & Ding, W. Several kinds of special least squares solutions to quaternion matrix equation \(AXB=C\). J. Appl. Math. Comput. 68, 1881–1899 (2022). https://doi.org/10.1007/s12190-021-01591-0

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  • DOI: https://doi.org/10.1007/s12190-021-01591-0

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