AI 中文总结
研究对偶矩阵的极分解，通过推导得出其极分解形式，并探讨存在性与唯一性条件，以构建的例子进行说明。
AI 中文摘要
形如\(a_s + a_d\epsilon\)（其中\(a_s, a_d \in\mathbb{C}^{n \times n}\)且\(\epsilon\)是满足\(\epsilon^2 = 0\)的无穷小单位）的数称为对偶数。以对偶数为元素的矩阵称为对偶矩阵。本文旨在推导对偶矩阵的极分解并研究其存在性与唯一性条件，还构建了一些例子来说明这些结果。
英文摘要
A number of the form $a_s+a_d ε$, where $a_s, a_d \in\mathbb{C}^{n \times n}$ and $ε$ is an infinitesimal unit satisfying $ε^2=0$, is called a dual number. A matrix with dual number entries is known as dual matrix. The objective of this article is to derive a polar decomposition of dual matrices and to study the existence and uniqueness conditions. To illustrate these results, some examples are constructed.
CommentsThis is a preliminary version of the manuscript. We intend to upload a revised version incorporating additional results and minor modifications
