A direct approach to the rational normal form

TL;DR

This paper presents a straightforward constructive proof for the existence and uniqueness of the rational normal form of a quadratic matrix, simplifying previous approaches.

Contribution

It introduces a direct, simplified proof for the rational normal form's existence and uniqueness, enhancing understanding and potential applications.

Findings

Proof of existence and uniqueness of rational normal form

Simplified constructive method for quadratic matrices

Potential for improved computational algorithms

Abstract

We give a short constructive proof for the existence and uniqueness of the rational normal form of a quadratic matrix.