|
|
![[parent]](http://images.planetmath.org:8080/images/uparrow.png) Viewing Correction to 'polarity'
|
Some generalizations by CWoo
Correction id: 8285
Filed on: 2006-06-15 17:17:12
Status: Accepted on 2006-06-17 13:32:00
Type: Addendum
Correction text:
Hi, you may want to mention that a duality can be defined between arbitrary projective geometries PG(V) and PG(W). You can then mention that in the case when W=V, then PG(V) is self-dual. Also, mention that in fact a duality can only exist when V and W are both finite dimensional (which confirms the condition that V be finite dimensional in your definition). Finally, in Remark 3, you can say that when PG(V) is self dual, points are called poles, and hyperplanes are called polars.
Chi |
Comment from object owner Algeboy:
Hi, you may want to mention that a duality can be defined between arbitrary projective geometries PG(V) and PG(W). You can then mention that in the case when W=V, then PG(V) is self-dual. Also, mention that in fact a duality can only exist when V and W are both finite dimensional (which confirms the condition that V be finite dimensional in your definition). Finally, in Remark 3, you can say that when PG(V) is self dual, points are called poles, and hyperplanes are called polars.
Chi
>> I think I got. |
|
|
|
|
|
|
|
|
|
|
