Angles between subspaces computed in Clifford Algebra

TL;DR

This paper reviews traditional methods for computing angles between subspaces and introduces a novel approach using Clifford algebra, which provides explicit and comprehensive information about their relative orientation.

Contribution

It presents a new Clifford algebra-based method for calculating subspace angles, offering clearer geometric interpretation and practical advantages over matrix algebra techniques.

Findings

Clifford algebra encodes full angular information between subspaces.

Geometric product yields explicit relative orientation data.

Method enhances understanding of subspace relationships.

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 practical access to the relative orientation information.