基于矩阵半张量积的求解八音矩阵方程 $$AXB=C$$ 的实数法

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-03-23 DOI:10.1007/s00006-024-01316-z

Xiaochen Liu, Ying Li, Wenxv Ding, Ruyu Tao

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引用次数: 0

摘要

本文基于矩阵的半张积研究了八音矩阵方程（AXB=C/）。首先，我们提出了八元数的左实元表示法和右实元表示法。然后，我们将这些表示与特殊矩阵的 $\mathcal {H}$表示相结合，得到了八音矩阵方程 $AXB=C$的最小二乘赫米解的表达式。最后，我们通过数值实验验证了我们方法的有效性和稳定性。

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

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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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.