Mathematical Methods in the Applied Sciences

RESEARCH ARTICLE

Semi-tensor product of quaternion matrices and its application

Xueling Fan

College of Mathematical Sciences, Liaocheng University, Shandong Research Center of Semi-tensor Product of Matrices: Theory and Applications, Liaocheng, China

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Ying Li,

Corresponding Author

Ying Li

[email protected]

orcid.org/0000-0003-1829-7327

College of Mathematical Sciences, Liaocheng University, Shandong Research Center of Semi-tensor Product of Matrices: Theory and Applications, Liaocheng, China

Correspondence

Ying Li, College of Mathematical Sciences, Liaocheng University, Shandong Research Center of Semi-tensor Product of Matrices: Theory and Applications, Liaocheng 252000, China.

Email: [email protected]

Communicated by: K. Gürlebeck

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Wenxv Ding,

Wenxv Ding

College of Mathematical Sciences, Liaocheng University, Shandong Research Center of Semi-tensor Product of Matrices: Theory and Applications, Liaocheng, China

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Jianli Zhao,

Jianli Zhao

College of Mathematical Sciences, Liaocheng University, Shandong Research Center of Semi-tensor Product of Matrices: Theory and Applications, Liaocheng, China

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Xueling Fan,

Xueling Fan

College of Mathematical Sciences, Liaocheng University, Shandong Research Center of Semi-tensor Product of Matrices: Theory and Applications, Liaocheng, China

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Ying Li,

Corresponding Author

Ying Li

[email protected]

orcid.org/0000-0003-1829-7327

College of Mathematical Sciences, Liaocheng University, Shandong Research Center of Semi-tensor Product of Matrices: Theory and Applications, Liaocheng, China

Correspondence

Ying Li, College of Mathematical Sciences, Liaocheng University, Shandong Research Center of Semi-tensor Product of Matrices: Theory and Applications, Liaocheng 252000, China.

Email: [email protected]

Communicated by: K. Gürlebeck

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Wenxv Ding,

Wenxv Ding

College of Mathematical Sciences, Liaocheng University, Shandong Research Center of Semi-tensor Product of Matrices: Theory and Applications, Liaocheng, China

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Jianli Zhao,

Jianli Zhao

College of Mathematical Sciences, Liaocheng University, Shandong Research Center of Semi-tensor Product of Matrices: Theory and Applications, Liaocheng, China

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First published: 01 December 2022

https://doi.org/10.1002/mma.8916

Funding information: This study is supported by the National Natural Science Foundation of China under Grant 62176112, the Natural Science Foundation of Shandong Province under Grants ZR2020MA053 and ZR2022MA030, and Discipline with Strong Characteristics of Liaocheng University Intelligent Science and Technology under Grant 319462208.

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Abstract

Unlike real or complex numbers, quaternion multiplication does not satisfy the commutative law. This makes it impossible to generalize some conclusions on semi-tensor product to quaternion directly, which is valid on real or complex number fields. In this paper, we define semi-tensor product of quaternion matrices and study the properties of semi-tensor product of quaternion matrices, and the conclusion is applied to the color digital image restoration model.

CONFLICT OF INTEREST

The authors declare that there are no conflict of interests to this work.

AUTHOR CONTRIBUTIONS

Xueling Fan provided the resources, prepared the software, supervised the study, validated the results, visualized the study, wrote the original draft of the manuscript, and reviewed and edited the manuscript. Ying Li, Wenxv Ding, and Jianli Zhao supervised the study.

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Volume46, Issue6

April 2023

Pages 6450-6462

Semi-tensor product of quaternion matrices and its application

Abstract

CONFLICT OF INTEREST

AUTHOR CONTRIBUTIONS

REFERENCES

References

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Semi-tensor product of quaternion matrices and its application

Abstract

CONFLICT OF INTEREST

AUTHOR CONTRIBUTIONS

REFERENCES

References

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