Warning

 

Close

Confirm Action

Are you sure you wish to do this?

Confirm Cancel
Member Login
Posted: 9/5/2010 9:50:54 AM EDT
[Last Edit: 9/5/2010 9:53:45 AM EDT by WildApple]
Are you smarter than a 5th grader?

Want to break this down for us then?

Projective linear group explained in plain English

http://en.wikipedia.org/wiki/Projective_linear_group

In mathematics, especially in the group theoretic area of algebra, the projective linear group (also known as the projective general linear group or PGL) is the induced action of the general linear group of a vector space V on the associated projective space P(V). Explicitly, the projective linear group is the quotient group

PGL(V) = GL(V)/Z(V)

where GL(V) is the general linear group of V and Z(V) is the subgroup of all nonzero scalar transformations of V; these are quotiented out because they act trivially on the projective space and they form the kernel of the action, and the notation "Z" is because the scalar transformations are the center of the general linear group.

The projective special linear group, PSL, is defined analogously, as the induced action of the special linear group on the associated projective space. Explicitly:

PSL(V) = SL(V)/SZ(V)

where SL(V) is the special linear group over V and SZ(V) is the subgroup of scalar transformations with unit determinant. Here SZ is the center of SL, and is naturally identified with the group of nth roots of unity in K (where n is the dimension and K is the base field).

PGL and PSL are some of the fundamental groups of study, part of the so-called classical groups, and an element of PGL is called a projective linear transformation. If V is the n-dimensional vector space over a field F, namely V = Fn, the alternate notations PGL(n, F) and PSL(n, F) are also used.

Note that PGL(n, F) and PSL(n, F) are equal if and only if every element of F contains a nth root in F. As an example, note that PGL(2,C)=PSL(2,C), but PGL(2,R)>PSL(2,R);[1] this corresponds to the real projective line being orientable, and the projective special linear group only being the orientation-preserving transformations.

PGL and PSL can also be defined over a ring, with the most important example being the modular group, PSL(2, Z).
Link Posted: 9/5/2010 9:53:12 AM EDT
[Last Edit: 9/5/2010 9:54:10 AM EDT by tweeter]
LOL, do you actually think that 5th graders LEARN that?

Hmm, sarcasm...
Link Posted: 9/5/2010 10:02:08 AM EDT
Maybe at 5th grade, starfleet/Vulcan prep school.

As far as public school 5th graders in USA? I am smarter than most 24th graders and I ain't that smart.
Link Posted: 9/5/2010 10:08:14 AM EDT
Originally Posted By tweeter:
LOL, do you actually think that 5th graders LEARN that?

Hmm, sarcasm...


tweeter, you appear to be a sarcastic A-hole ©

But then again, it looks like you know that already


IBKJ

In Before Kieth_J
Link Posted: 9/5/2010 4:08:05 PM EDT
Originally Posted By CarbineDad:
Originally Posted By tweeter:
LOL, do you actually think that 5th graders LEARN that?

Hmm, sarcasm...


tweeter, you appear to be a sarcastic A-hole ©

But then again, it looks like you know that already


IBKJ

In Before Kieth_J



I think Keith could make Stephen Hawking's head explode.

Even the Speak-and-Spell voicebox thingie would call him Daddy.
Link Posted: 9/5/2010 4:30:38 PM EDT
As long as I get to pick the 5th grader, sure!
Link Posted: 9/5/2010 4:36:07 PM EDT
This is GD.

Everyone here is smarter than a 5th grader.

Oops, wait....wrong forum.
My bad..
Link Posted: 9/5/2010 4:49:40 PM EDT
Second one in? Sure.


Top Top