Projective linear group

Given a vector space $V$ the projective linear group or projective general linear group is

P G L (V) = G L (V) / Z (V)

where $G L (V)$ is the general linear group of $V$ and $Z (V)$ is the subgroup of all nonzero scalar transformations of $V$ (which is the center of this group). Their elements are called homographies.

It acts on the projective space associated to $V$ , $P (V)$ , in the following way. Given $[T] \in P G L (V)$ we have

[T] [Z] = [T (Z)]

for $[Z] \in P (V)$ .

In case $V = C^{2}$ we have the Moebius transformations.