On similar matrices over the dual numbers

TL;DR

This paper studies matrices over dual numbers, proposing a classification method up to similarity, and explicitly constructs canonical forms for matrices of sizes 2 and 3.

Contribution

It introduces a new approach to classify dual number matrices up to similarity and provides explicit canonical forms for small sizes.

Findings

Canonical matrices of order 2 and 3 are explicitly constructed.

Preliminary results demonstrate the feasibility of the classification approach.

Abstract

Matrices over the dual numbers are considered. We propose an approach to classify these matrices up to similarity. Some preliminary results on the realization of this approach are obtained. In particular, we produce explicitly canonical matrices of orders 2 and 3.