{"title":"A Real Method for Solving Octonion Matrix Equation \\(AXB=C\\) Based on Semi-tensor Product of Matrices","authors":"Xiaochen Liu, Ying Li, Wenxv Ding, Ruyu Tao","doi":"10.1007/s00006-024-01316-z","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, the octonion matrix equation <span>\\(AXB=C\\)</span> 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 <span>\\(AXB=C\\)</span> by combining these representations with <span>\\(\\mathcal {H}\\)</span>-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 <span>\\(AXB=C.\\)</span> Finally, the validity and stability of our method is verified by numerical experiments.</p></div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"34 2","pages":""},"PeriodicalIF":1.1000,"publicationDate":"2024-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Applied Clifford Algebras","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00006-024-01316-z","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
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.
期刊介绍：
Advances in Applied Clifford Algebras (AACA) publishes high-quality peer-reviewed research papers as well as expository and survey articles in the area of Clifford algebras and their applications to other branches of mathematics, physics, engineering, and related fields. The journal ensures rapid publication and is organized in six sections: Analysis, Differential Geometry and Dirac Operators, Mathematical Structures, Theoretical and Mathematical Physics, Applications, and Book Reviews.
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