Hyperorthogonal family of vectors and the associated Gram matrix

Bent Fuglede

doi:10.4171/lem/60-1/2-3

Hyperorthogonal family of vectors and the associated Gram matrix

Department of Mathematical Sciences

Abstract

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

Original language	English
Journal	L’Enseignement Mathématique
Volume	60
Issue number	1/2
Pages (from-to)	31-41
ISSN	0013-8584
DOIs	https://doi.org/10.4171/lem/60-1/2-3
Publication status	Published - 2014

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10.4171/lem/60-1/2-3

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

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

U2 - 10.4171/lem/60-1/2-3

DO - 10.4171/lem/60-1/2-3

M3 - Journal article

SN - 0013-8584

VL - 60

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EP - 41

JO - Enseignement Mathematique

JF - Enseignement Mathematique

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