In the field of representation theory in mathematics, a projective representation of a group G on a vector space V over a field F is a group homomorphism from G to the projective linear group

PGL(V, F) = GL(V, F) / F^*,

where GL(V, F) is the general linear group of invertible linear transformations of V over F and F^* is the normal subgroup consisting of multiplications of vectors in V by nonzero elements of F (that is, scalar multiples of the identity; scalar transformations).