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Dimension of the intersection of a pair of orthogonal groups

AuthorsSong, Seok-Zun; Durán Díaz, Raúl; Hernández Encinas, Luis; Muñoz Masqué, Jaime; Queiruga Dios, Araceli
KeywordsDiagonalizable endomorphism
Matrix exponential
Orthogonal group
Symmetric bilinear form
Issue Date12-Nov-2009
SeriesInternational Journal of Computer Mathematics
AbstractLet $g,h\colon V\times V\rightarrow mathbb{C}$ 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 $L\colon \rightarrow V$ associated to $g,h$ is diagonalizable, then the dimension of the intersection group $G\cap H$ is computed in terms of the dimensions of the eigenspaces of $L$.
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