Talk:Projective space/Archive 1

reminder to self
(or whoever else wants to edit this) I want to put something about notation. Introduce the notation P(V) (which is used in the text, but not defined. Then the notation KP^n.  Also mention that P^n without qualification means complex projective.  Though they have their own article, homogeneous coordinates need more explanation in this one.  When you add that, add the useless fact that homogeneous coordinates are not actually coordinates, they are instead elements of the dual space V*.  I'm getting on a plane in 20 minutes, but I should do this when I get home.  See also the planetmath article.  -Lethe | Talk 03:44, 27 July 2005 (UTC)

Remark
It's necessary that $T:V\to W$ let be one-to-one. —Preceding unsigned comment added by Molinagaray (talk • contribs)


 * What does "highly symmetric" mean? Please be more exact! 134.169.128.67 09:56, 22 September 2006 (UTC)

2 Questions
First, why say "vector space over a division ring" when this is improper, and further, the vector space page inconsistently (but correctly) builds on a field. More accurately, one should say module over a division ring, and of course, it would be more than acceptable to mention that this is as a vector space missing merely scalar commutativity. Second, why is that previous statement qualified by "in particular over a field"? Over a field, we have affine space, which is not isomorphic to the projective space, as even stated throughout the article (by mentioning that the projective plane is an affine plane unioned with a line at infinity.) 12.147.134.239 04:19, 4 May 2007 (UTC)


 * I also found the division ring showing up in the first place a bit distracting. I moved this to the main text and also replaced vector space over a division ring by module over a d.r. Jakob.scholbach 02:05, 5 May 2007 (UTC)

Merging with axiomatic projective space
There is already another article on projective spaces, poetntially they could be merged. For now i've just added the alternative approach section with a reference to the other definition.--Kmhkmh 05:14, 4 March 2007 (UTC)


 * That's the projective geometry article. It's definitely time to bring them together. — Preceding unsigned comment added by 64.132.207.253 (talk) 14:30, 16 June 2007 (UTC)