matrix representation

A matrix representationPlanetmathPlanetmath of a group G is a group homomorphismMathworldPlanetmath between G and GLn(), that is, a function


such that

  • X(gh)=X(g)X(h),

  • X(e)=I

Notice that this definition is equivalentMathworldPlanetmathPlanetmathPlanetmathPlanetmath to the group representationMathworldPlanetmathPlanetmath definition when the vector spaceMathworldPlanetmath V is finite dimensional over . The parameter n (or in the case of a group representation, the dimensionPlanetmathPlanetmath of V) is called the degree of the representation.


  • 1 Bruce E. Sagan. The Symmetric GroupMathworldPlanetmathPlanetmath: Representations, Combinatorial AlgorithmsMathworldPlanetmath and Symmetric Functions. 2a Ed. 2000. Graduate Texts in Mathematics. Springer.
Title matrix representation
Canonical name MatrixRepresentation
Date of creation 2013-03-22 14:53:56
Last modified on 2013-03-22 14:53:56
Owner drini (3)
Last modified by drini (3)
Numerical id 9
Author drini (3)
Entry type Definition
Classification msc 20C99
Related topic PermutationRepresentation