On the Jordan--Chevalley decomposition of a matrix

TL;DR

This paper presents an elegant algorithmic proof for the Jordan--Chevalley decomposition of matrices, revising previous discussions and highlighting the historical roots of the method.

Contribution

It offers a refined, algorithmic proof of the Jordan--Chevalley decomposition, building on and slightly revising prior work by Couty, Esterle, and Zarouf.

Findings

Provides an elegant, algorithmic proof of the decomposition.

Revises and clarifies previous discussions on the method.

Highlights historical origins dating back to Chevalley (1951).

Abstract

The purpose of this note is to advertise an elegant algorithmic proof for the Jordan--Chevalley decomposition of a matrix, following and (slightly) revising the discussion of Couty, Esterle und Zarouf (2011). The basic idea of that method goes back to Chevalley (1951).