Classification of pairs of rotations in finite-dimensional Euclidean space

TL;DR

This paper provides a comprehensive classification of all pairs of rotations in finite-dimensional Euclidean spaces, considering their behavior under simultaneous conjugation by orthogonal transformations.

Contribution

It introduces a complete classification scheme for pairs of rotations in Euclidean spaces, up to simultaneous orthogonal conjugation, expanding understanding of their structural relationships.

Findings

Classification of all pairs of rotations in finite-dimensional Euclidean space.

Characterization of pairs of rotations up to simultaneous orthogonal conjugation.

Framework for analyzing relationships between rotation pairs in Euclidean spaces.

Abstract

A rotation in a Euclidean space V is an orthogonal map on V which acts locally as a plane rotation with some fixed angle. We give a classification of all pairs of rotations in finite-dimensional Euclidean space, up to simultaneous conjugation with orthogonal maps.