Examples
Consider the complex number u = e2πi / 3 which has the property u3 = 1. The cyclic group C3 = {1, u, u2} has a representation ρ on C2 given by:
This representation is faithful because ρ is a one-to-one map.
An isomorphic representation for C3 is
The group C3 may also be faithfully represented on R2 by
where and .
Read more about this topic: Group Representation
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