On Polar Decomposition of Dual Matrices

Abstract

A number of the form $a_s+a_d\epsilon$, where $a_s,a_d\in {\mathbb{C}}^{n\times n}$ and $\epsilon$ is an infinitesimal unit satisfying ${\epsilon }^2=0$, 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.

arXiv commentThis is a preliminary version of the manuscript. We intend to upload a revised version incorporating additional results and minor modifications