Dimension of the intersection of a pair of orthogonal groups

Let g, h:V×V→ℂ be two non-degenerate symmetric bilinear forms on a finite-dimensional complex vector space V. Let G (resp. H) be the Lie group of isometries of g (resp. h). If the endomorphism L:V→V associated to g, h is diagonalizable, then the dimension of the intersection group G∩H is computed in...

Full description

Saved in:

Bibliographic Details
Published in:	International journal of computer mathematics Vol. 86; no. 10-11; pp. 1678 - 1683
Main Authors:	Song, Seok-Zun, Díaz, R. Durán, Encinas, L. Hernández, Masqué, J. Muñoz, Dios, A. Queiruga
Format:	Journal Article
Language:	English
Published:	Abingdon Taylor & Francis 01-11-2009 Taylor & Francis Ltd
Subjects:	diagonalizable endomorphism Eigenvalues isometry Mathematics matrix exponential orthogonal group symmetric bilinear form Vector space
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Description
Summary:	Let g, h:V×V→ℂ be two non-degenerate symmetric bilinear forms on a finite-dimensional complex vector space V. Let G (resp. H) be the Lie group of isometries of g (resp. h). If the endomorphism L:V→V associated to g, h is diagonalizable, then the dimension of the intersection group G∩H is computed in terms of the dimensions of the eigenspaces of L.
ISSN:	0020-7160 1029-0265
DOI:	10.1080/00207160802706583