A parametrization of matrix conjugacy orbit sets as unions of affine planes

TL;DR

This paper introduces a new canonical form for complex matrices under conjugacy, representing the set of matrices as a union of affine planes, simplifying the classification problem.

Contribution

It provides a novel parametrization of matrix conjugacy orbit sets as unions of affine planes, offering a new canonical form for matrices over algebraically closed fields.

Findings

Canonical form expressed as union of affine planes

Simplifies classification of matrices up to conjugacy

Applicable over algebraically closed fields

Abstract

The problem of finding a canonical form of complex matrices up to conjugacy with the set of canonical matrices being a union of affine planes in the matrix space is considered. A solution of the problem is given producing a new canonical form for matrices over algebraically closed fields.