JournalslemVol. 60, No. 1/2pp. 31–41

Hyperorthogonal family of vectors and the associated Gram matrix

  • Bent Fuglede

    University of Copenhagen, Denmark
Hyperorthogonal family of vectors and the associated Gram matrix cover

Abstract

A family of non-zero vectors in Euclidean nn-space is termed hyperorthogonal if the angle between any two distinct vectors of the family is at least π/2\pi /2. Any hyperorthogonal family is finite and contains at most 2n2n vectors. It decomposes uniquely into the union of mutually orthogonal irreducible subfamilies. An equivalent formulation in terms of the associated Gram matrix is given.

Cite this article

Bent Fuglede, Hyperorthogonal family of vectors and the associated Gram matrix. Enseign. Math. 60 (2014), no. 1, pp. 31–41

DOI 10.4171/LEM/60-1/2-3