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...
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| Published in: | International journal of computer mathematics Vol. 86; no. 10-11; pp. 1678 - 1683 |
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| Main Authors: | , , , , |
| Format: | Journal Article |
| Language: | English |
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Taylor & Francis
01-11-2009
Taylor & Francis Ltd |
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| Abstract | 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. |
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| AbstractList | Let g, h:VtimesV[arrow right]Copf 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[arrow right]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. [PUBLICATION ABSTRACT] 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. |
| Author | Díaz, R. Durán Encinas, L. Hernández Dios, A. Queiruga Song, Seok-Zun Masqué, J. Muñoz |
| Author_xml | – sequence: 1 givenname: Seok-Zun surname: Song fullname: Song, Seok-Zun organization: Department of Mathematics , Cheju National University – sequence: 2 givenname: R. Durán surname: Díaz fullname: Díaz, R. Durán organization: Departamento de Automática , University of Alcalá, Campus Universitario N-II – sequence: 3 givenname: L. Hernández surname: Encinas fullname: Encinas, L. Hernández email: luis@iec.csic.es organization: Department of Information Processing and Coding , Applied Physics Institute, CSIC – sequence: 4 givenname: J. Muñoz surname: Masqué fullname: Masqué, J. Muñoz organization: Department of Information Processing and Coding , Applied Physics Institute, CSIC – sequence: 5 givenname: A. Queiruga surname: Dios fullname: Dios, A. Queiruga organization: Department of Applied Mathematics, E.T.S.I.I. , University of Salamanca |
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| Copyright | Copyright Taylor & Francis Group, LLC 2009 Copyright Taylor & Francis Ltd. Oct 2009 |
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| Snippet | 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... Let g, h:VtimesV[arrow right]Copf be two non-degenerate symmetric bilinear forms on a finite-dimensional complex vector space V. Let G (resp. H) be the Lie... |
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| SubjectTerms | diagonalizable endomorphism Eigenvalues isometry Mathematics matrix exponential orthogonal group symmetric bilinear form Vector space |
| Title | Dimension of the intersection of a pair of orthogonal groups |
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