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Equiangular Subspaces in Euclidean Spaces

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.

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Author information

Correspondence to Benny Sudakov.

Additional information

Research supported in part by SNSF Grant 200021-175573.

Editor in Charge: János Pach

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Cite this article

Balla, I., Sudakov, B. Equiangular Subspaces in Euclidean Spaces. Discrete Comput Geom 61, 81–90 (2019). https://doi.org/10.1007/s00454-018-9972-5

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Keywords

  • Equiangular lines
  • Subspaces
  • Grassmannian
  • Principal angles
  • Polynomial method

Mathematics Subject Classification

  • 52C35
  • 05D99