On Polar Decomposition of Dual Matrices

V. Bhagyalakshmi; T. Kurmayya

On Polar Decomposition of Dual Matrices

Rings and Algebras 2026-07-10 v1

Authors: V. Bhagyalakshmi , T. Kurmayya

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.

Keywords

dual numbers dual matrices polar decomposition matrix analysis infinitesimal

Cite

@article{arxiv.2607.09302,
  title  = {On Polar Decomposition of Dual Matrices},
  author = {V. Bhagyalakshmi and T. Kurmayya},
  journal= {arXiv preprint arXiv:2607.09302},
  year   = {2026}
}

Comments

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