# Equiangular subspaces in Euclidean spaces

## TL;DR

This paper extends the concept of equiangular lines to equiangular subspaces in Euclidean spaces, providing new bounds and insights into their maximum sizes.

## Contribution

It introduces natural definitions of angles between subspaces and improves existing bounds on the maximum size of equiangular subspace sets.

## Key findings

- Extended bounds on the size of equiangular subspace sets
- Improved upon previous results by Blokhuis
- Provided new methods for defining angles between subspaces

## Abstract

A set of lines through the origin is called equiangular if every pair of lines defines the same angle, and the maximum size of an equiangular set of lines in $\mathbb{R}^n$ was studied extensively for the last 70 years. In this paper, we study analogous questions for $k$-dimensional subspaces. We discuss natural ways of defining the angle between $k$-dimensional subspaces and correspondingly study the maximum size of an equiangular set of $k$-dimensional subspaces in $\mathbb{R}^n$. Our bounds extend and improve a result of Blokhuis.