From trivial spectrum subspaces to spaces of diagonalizable real matrices

TL;DR

This paper presents a new proof for classifying maximal-dimensional subspaces of diagonalizable real matrices, extending Gerstenhaber's theorem to a broader context involving spectrum subspaces.

Contribution

It introduces a novel approach that generalizes Gerstenhaber's theorem to classify diagonalizable matrix subspaces with maximal dimension.

Findings

Provides a new proof for the classification of maximal diagonalizable subspaces

Extends Gerstenhaber's theorem to spectrum subspaces

Establishes a connection between trivial spectrum subspaces and diagonalizable matrices

Abstract

A recent generalization of Gerstenhaber's theorem on spaces of nilpotent matrices is shown to yield a new proof of the classification of linear subspaces of diagonalizable real matrices with the maximal dimension.