A note on orthogonality of subspaces in Euclidean geometry

TL;DR

This paper explores how high-dimensional Euclidean geometry can be represented through the orthogonality relations of subspaces with specific dimensions and their intersections.

Contribution

It introduces a framework to describe Euclidean geometry using orthogonality of subspaces with fixed dimensions and intersections.

Findings

Euclidean geometry can be modeled via subspace orthogonality.

Orthogonality relations characterize geometric structures.

The approach simplifies understanding high-dimensional Euclidean spaces.

Abstract

We show that Euclidean geometry in suitably high dimension can be expressed as a theory of orthogonality of subspaces with fixed dimensions and fixed dimension of their meet.