Analisis Keberhinggaan Matriks Representasi atas Grup Berhingga

Abstract

Representation of a finite group G over generator linear non singular mxm matrix with entries of field K defined by group homomorphism A : G → GL m (K) Basically, the non singular mxm matrix A(x) which representing the finite group G divided into two, that are the unitary matrix and non unitary matrix . If A(x) is a non unitary matrix, then there exist a unitary matrix which similar to A(x). This research deals to analyze the numbers of one example of a unitary matrix representation over arbitrary finite group G with order n that is permutation matrix, and the number of unitary matrix which is similar to real non unitary matrix representation of arbitrary finite group G order 2. The results showed the numbers of permutation matrix representation is n! and unitary matrix which is similar to non unitary matrix representation is 2.