## Abstract

A family of lines through the origin in a Euclidean space is called equiangular if any pair of lines defines the same angle. The problem of estimating the maximum cardinality of such a family in R^{n} was studied extensively for the last 70 years. Motivated by a question of Lemmens and Seidel from 1973, we prove that for every fixed angle θ and n sufficiently large, there are at most 2n−2 lines in R^{n} with common angle θ. Moreover, this is achievable only for θ=arccos[Formula presented]. We also 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 R^{n}, obtaining bounds which extend and improve a result of Blokhuis.

Original language | English |
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Pages (from-to) | 85-91 |

Number of pages | 7 |

Journal | Electronic Notes in Discrete Mathematics |

Volume | 61 |

DOIs | |

State | Published - Aug 2017 |

Externally published | Yes |

## Keywords

- Euclidean spaces
- Grassmannian
- equiangular lines
- equiangular subspaces
- principle angles
- projective spaces