Angles between subspaces

TL;DR

This paper reviews the concept of angles between subspaces, introduces algebraic descriptions using Grassmann and Clifford algebras, and explains how the geometric product encodes complete relative angular information.

Contribution

It provides a comprehensive algebraic framework for understanding and computing angles between subspaces using Grassmann and Clifford algebra.

Findings

Geometric product encodes full relative angular information

Provides explicit computation methods for subspace angles

Offers a unified algebraic perspective on subspace orientation

Abstract

We first review the definition of the angle between subspaces and how it is computed using matrix algebra. Then we introduce the Grassmann and Clifford algebra description of subspaces. The geometric product of two subspaces yields the full relative angular information in an explicit manner. We explain and interpret the result of the geometric product of subspaces gaining thus full access to the relative orientation information.