projective plane

mathematics The space of equivalence classes of vectors

under non-zero scalar multiplication. Elements are sets of

the form

kv: k != 0, k scalar, v != O, v a vector

where O is the origin. v is a representative member of this

equivalence class.

The projective plane of a vector space is the collection of

its 1-dimensional subspaces. The properties of the vector

space induce a topology and notions of smoothness on the

projective plane.

A projective plane is in no meaningful sense a plane and would

therefore be (but isn't) better described as a "projective

space".

(1996-09-28)