A geometric decomposition of real diagonalizable matrices with complex eigenvalues

TL;DR

This paper introduces a real, coordinate-free geometric decomposition for real diagonalizable matrices with complex eigenvalues, offering a new perspective on their structure.

Contribution

It provides the first geometric, coordinate-free decomposition of such matrices, enhancing understanding of their structure and properties.

Findings

Decomposition is coordinate-free and geometrically interpretable.

Applicable to all real diagonalizable matrices with complex eigenvalues.

Facilitates better understanding of matrix structure in real vector spaces.

Abstract

For any real diagonalizable matrix with complex eigenvalues we provide a real, coordinate free decomposition with a clear geometric interpretation.