Definition:Projective Plane

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Definition

Let $\FF$ be a field whose zero is $0$.

The projective plane over $\FF$ is the set of points represented by ordered triples $\tuple {x, y, z}$ such that:

$x, y, z$ are not all equal to $0$
$x, y, z \in \FF$
for $\lambda \in \FF$ such that $\lambda \ne 0$, the ordered triples $\tuple {x, y, z}$ and $\tuple {\lambda x, \lambda y, \lambda z}$ represent the same point.


Real Projective Plane

The real projective plane $\R P^2$ is the projective plane over the field of real numbers.


Complex Projective Plane

The complex projective plane $\C P^2$ is the projective plane over the field of complex numbers.


Finite Projective Plane

Let $\GF$ be a finite field.

Let $P$ be the projective plane over $\GF$.

Then $P$ is known as a finite projective plane.


Examples

Projective Plane/Examples

Also see

  • Results about projective planes can be found here.


Sources