matrix representation (original) (raw)

A matrix representation of a group G is a group homomorphism between G and G⁢Ln⁢(ℂ), that is, a function

such that

• •
  X⁢(g⁢h)=X⁢(g)⁢X⁢(h),
• •
  X⁢(e)=I

Notice that this definition is equivalent to the group representation definition when the vector space V is finite dimensional over ℂ. The parameter n (or in the case of a group representation, the dimension of V) is called the degree of the representation.

References

• 1 Bruce E. Sagan. The Symmetric Group: Representations, Combinatorial Algorithms and Symmetric Functions. 2a Ed. 2000. Graduate Texts in Mathematics. Springer.