On matrix representation of some finite groups
Abstract
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 Kisomorphism 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.
 Publication:

Research in Mathematical Sciences: A Catalyst for Creativity and Innovation
 Pub Date:
 April 2013
 DOI:
 10.1063/1.4801246
 Bibcode:
 2013AIPC.1522.1055M
 Keywords:

 group theory;
 matrix algebra;
 vectors;
 02.10.Ud;
 02.10.Yn;
 02.20.a;
 Linear algebra;
 Matrix theory;
 Group theory