On Polar Decomposition of Dual Matrices

Abstract

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.