On matrix representation of some finite groups
A homomorphism T:g→T(g) of G into GL(M) is a representation of G with representation space M. Two representations T and T′ with space M and M′ are said to be equivalent if there exists a K-isomorphism S of M and M′. The notation (M:K) is the dimension of M over K where M is a vector space and K is a...
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| Main Authors: | , , , , |
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| Format: | Conference or Workshop Item |
| Published: |
2013
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| Subjects: | |
| Online Access: | http://eprints.utm.my/id/eprint/51212/ http://dx.doi.org/10.1063/1.4801246 |
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| Institution: | Universiti Teknologi Malaysia |
| Summary: | A homomorphism T:g→T(g) of G into GL(M) is a representation of G with representation space M. Two representations T and T′ with space M and M′ are said to be equivalent if there exists a K-isomorphism S of M and M′. The notation (M:K) is the dimension of M over K where M is a vector space and K is a field while G is a finite group. A matrix representation of G of degree n is a homomorphism T:g→T(g) of G into GL(n, K), where GL(n, K) stands for the group of invertible n × n matrices over K. In this paper, the matrix representations for dihedral groups of order 12 and order 16 and an alternating group of order 12 are presented. |
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