# Server problems

We had some server problems and are working on it. Sorry for the inconvenience.

# Lecture 7

Definition (complete quadrilateral). A configuration consisting of four lines in the projective plane – no three through one point – and the six intersection points, one for each pair of lines, form a complete quadrilateral. # Room changes

Sorry for the inconvenience today. The other dates that we have to leave the regular room are:

Monday 10.12. MA 649

Thursday 13.12. MA 650

# Projective transformations

Let $V$, $W$ be two vectorspaces over the same field and of the same dimension and $F\colon V \rightarrow W$ a linear isomorphism. In particular $ker(F) = \{0\}$, so F maps 1-dimensional subspaces to 1-dimensional subspaces.

Hence $F$ induces a map from $P(V)$ to $P(W)$.

Definition: A projective transformation $f$ from $P(V)$ to $P(W)$ is a map defined by a linear isomorphism $F\colon V \rightarrow W$ such that

\begin{equation*}
f([v]) = [F(v)] \quad \forall [v] \in P(V)\,.