Vol. 73, No. 1, 1977

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Generating O(n) with reflections

Morris Leroy Eaton and Michael David Perlman

Vol. 73 (1977), No. 1, 73–80
Abstract

For r Cn ≡{x|x Rn,x= 1}, let Sr = In 2rrwhere r is a column vector. O(n) denotes the orthogonal group on Rn. If R Cn, let = {Sr|r R} and let G be the smallest closed subgroup of O(n) which contains . G is reducible if there is a nontrivial subspace M Rn such that gM M for all g G. Otherwise, G is irreducible.

Theorem. If G is infinite and irreducible, then G = O(n).

Mathematical Subject Classification 2000
Primary: 20H20
Milestones
Received: 11 February 1977
Revised: 28 July 1977
Published: 1 November 1977
Authors
Morris Leroy Eaton
Michael David Perlman