论文标题
von Neumann类型的痕量不等式的双重四元素矩阵
von Neumann type trace inequality for dual quaternion matrices
论文作者
论文摘要
双重四基矩阵在多代理形成控制中具有重要的应用。在本文中，我们首先介绍了双重四基矩阵光谱规范的概念。然后，我们引入了von Neumann类型的痕量不平等和霍夫曼 - 韦兰特类型的不等式，用于一般双重四元素矩阵，后者是在双重Quaternion矩阵的所有奇异值上同时表征的同时扰动。特别是，我们还介绍了上述两个不平等的变体，这两个不等式由双重四基因遗传学矩阵的特征值表示。我们的结果有助于进一步研究双重四基矩阵理论，算法设计和应用。
Dual quaternion matrices have important applications in multi-agent formation control. In this paper, we first address the concept of spectral norm of dual quaternion matrices. Then, we introduce a von Neumann type trace inequality and a Hoffman-Wielandt type inequality for general dual quaternion matrices, where the latter characterizes a simultaneous perturbation bound on all singular values of a dual quaternion matrix. In particular, we also present two variants of the above two inequalities expressed by eigenvalues of dual quaternion Hermitian matrices. Our results are helpful for the further study of dual quaternion matrix theory, algorithmic design, and applications.
