Projective Geometry
Let us start with a general definition for an arbitrary projective space. In this lecture we will almost entirely deal with real projective spaces.
Definition. Let $V$ be a vector space over an arbitrary field $F$. The projective space $P(V)$ is the set of $1$-dimensional vector subspaces of $V$. If $\dim(V) = n+1$, then the dimension of the projective space is $n$.
- A $1$-dimensional projective space is a projective line.
- A $2$-dimensional projective space is a projective plane.