Heya, folks. I just realized that what I did above was wrong .
Anyway, I tried to find that article on the web but couldn't. Try googling for something like "Zeilberger+WZ+proof+Riemann+Hypothesis". I turned up a ps doc at "www.math.rutgers.edu/~zeilberg/mamarim/mamarimPS/rh.ps" and had to download GhostView to read it. Or you can try "www.math.rutgers.edu/~zeilberger/papers1.html", which also has alot of other cool stuff on it BTW. Sorry, 'bout the let down. That's all I could find without looking too hard. Like I said before, I don't understand what Zeilberger is talking about, so I can't say whether the Riemann Hypothesis is really proven or not.

EDIT: I didn't know you couldn't link outside of GameDev!?

20: ...Qg2 ++

[edited by - GaulerTheGoat on May 31, 2003 10:40:20 PM]

quote:Original post by Anonymous Poster

quote:Original post by GaulerTheGoat
I just started getting more interested in vector spaces. Tell me how I am doing :

Vector differences are independant of the origin, so choose m . So
||u -m || = ||v -m || implies that
||u || = ||v ||. Multiplying out the norms
(u -m )•(u -m ) =
(v -m )•(v -m ) or
u •u -2u •m +m •m =
v •v -2v •m +m •m or
u •m = v •m .
The other equation gives similarly,
u •m'' = v •m'' .
Subtracting these two and factoring out the u on the LHS and the v on the RHS, and then subtracting the RHS and factoring out the m -m'' gives
(u -v )•(m -m'' ) = 0.

20: ...Qg2 ++

I''m not sure where you''re getting

||u || = ||v ||

but you don''t need it anyway. If you subtract the two equations at the end those two terms drop out because they are in both equations:

This:
u •u -2u •m +m •m =
v •v -2v •m +m •m

And this:
u •u -2u •m'' +m'' •m'' =
v •v -2v •m'' +m'' •m''

Yeah, that made its way into my brain while I was typing up this other post. For some reason ||u || = ||v || just popped into my head and I went with it. I am researching affine spaces right now and I kept thinking, "origins don''t matter." They were feeling negleted . Of course, like you said, it isn''t even neccessary . Can I give myself partial credit on this one?

20: ...Qg2 ++

AP: scalars are elements from any fully ordered body, because you need the positivity result to define the scalar product. Also, IIRC, Hermitte inner product is defining using a cosinus, and so is the scalar product (in fact, you can define a scalar product using a formula and from that formula define the cosinus in a particular space. For example, cosinus in C: [0,1] -> IR).

GaulerTheGoat: To link outside of gamedev, don't forget the "http://"... Besides, you can indeed call in an affine space (you can usually build one from an euclidean space anyway). But for the "origin doesn't matter" thing, you applied it wrong.

v = v + 0 if origin is 0, v = (v - m) + m if origin is m
m = m + 0 if origin is 0, m = 0 + m if origin is m

Therefore, ||v - m|| = ||v - m + 0|| : indeed vector differences DO NOT change. You almost got it right, but credits go to AP...

EDIT : additional question : let IM be the set of all vectors m defined the previous way, what is the dimension of IM?

ToohrVyk



[edited by - ToohrVyk on June 1, 2003 4:55:55 AM]