基于矩阵半张量积的求解八音矩阵方程 $$AXB=C$$ 的实数法

IF 1.1 2区数学 Q2 MATHEMATICS, APPLIED

Advances in Applied Clifford Algebras 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

Advances in Applied Clifford Algebras 数学-物理：数学物理

CiteScore

2.20

自引率

13.30%

发文量

审稿时长

3 months

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.