Equiangular lines and subspaces in Euclidean spaces

Igor Balla, Felix Dräxler, Peter Keevash, Benny Sudakov

Research output: Contribution to journalArticlepeer-review


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 Rn 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 Rn 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 Rn, obtaining bounds which extend and improve a result of Blokhuis.

Original languageEnglish
Pages (from-to)85-91
Number of pages7
JournalElectronic Notes in Discrete Mathematics
StatePublished - Aug 2017
Externally publishedYes


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


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