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

Institut for Matematiske Fag

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.

Originalsprog	Engelsk
Tidsskrift	L’Enseignement Mathématique
Vol/bind	60
Udgave nummer	1/2
Sider (fra-til)	31-41
ISSN	0013-8584
DOI	https://doi.org/10.4171/lem/60-1/2-3
Status	Udgivet - 2014

Adgang til dokumentet

10.4171/lem/60-1/2-3

Citationsformater

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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.

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

M3 - Journal article

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JO - Enseignement Mathematique

JF - Enseignement Mathematique

IS - 1/2

ER -