Projective Space

A projective space is a space that is invariant under the group  of all general linear homogeneous transformation in the space concerned, but not under all the transformations of any group containing  as a subgroup.

A projective space is the space of one-dimensional vector subspaces of a given vector space. For real vector spaces, the notation  or  denotes the real projective space of dimension  (i.e., the space of one-dimensional vector subspaces of ) and  denotes the complex projective space of complex dimension  (i.e., the space of one-dimensional complex vector subspaces of ).  can also be viewed as the set consisting of  together with its points at infinity.