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
Also see
- Results about projective planes can be found here.
Sources
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): projective plane