Dual quaternion matrix decompositions have played a crucial role in fields such as formation control and image processing in recent years. In this paper, we present an eigenvalue decomposition algorithm for dual quaternion Hermitian matrices. The proposed algorithm is founded on the structure-preserving tridiagonalization of the dual matrix representation of dual quaternion Hermitian matrices through the application of orthogonal matrices. Owing to the utilization of orthogonal transformations, the algorithm exhibits numerical stability. Numerical experiments are provided to illustrate the efficiency of the structure-preserving algorithm.

中文翻译：

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一种用于对偶四元数 Hermitian 特征值问题的新结构保持方法


近年来，双四元数矩阵分解在编队控制和图像处理等领域发挥了至关重要的作用。在本文中，我们提出了一种用于对偶四元数 Hermitian 矩阵的特征值分解算法。所提出的算法建立在通过应用正交矩阵对双四元数埃尔米特矩阵的对偶矩阵表示进行结构保持的三对角化之上。由于利用了正交变换，该算法表现出数值稳定性。提供了数值实验来说明结构保持算法的效率。