example of matrix representations
The function is a group homomorphism between and (that is invertible matrices of size , which is the set of non-zero complex numbers). And thus we say that carries a representation of the symmetric group.
Defining representation of
For each , let the function given by where is the permutation matrix given by
Such matrices are called permutation matrices because they are obtained permuting the colums of the identity matrix. The function so defined is then a group homomorphism, and thus carries a representation of the symmetric group.
|Title||example of matrix representations|
|Date of creation||2013-03-22 14:53:31|
|Last modified on||2013-03-22 14:53:31|
|Last modified by||drini (3)|