5
Name:
Anonymous
2008-07-17 17:08
>>4
How come it is like linear algebra but better
It is just more general approach that is easier to understand geometrically
Tell me the meaning of the cross product? Or the dot product? These are all specific or convoluted cases of Geometric Algebras simple constructs.
Cross product = Spanning and taking the orthogonal complement easily done in Geometric Algebra
(a^b) contracted from inverse of the superscalar
Dot product is easier in Geometric Algebra and has actual meaning for blades by use of the scalar product.
8
Name:
Anonymous
2008-07-17 19:08
>>6
no cross product in 4d
do you mean wedge product?
>>5
you can't just say that something is 'better' than something like linear algebra. linear algebra is fucking huge. scalar and vector products are more the domain of vector calc and analysis than linear algebra. now, inner products are linear algebra.
Also, how would you deal with all that matrix shit(arithmetic, transformations, determinants, diagonalizations, eigengarbage, singular values, etc) geometrically?
10
Name:
Anonymous
2008-07-17 19:48
[math] [B] [B] [B] [/math]
11
Name:
Anonymous
2008-07-17 20:12
>>9
alternating multilinear form and so on...
just actually looked up what geometric algebra actually was, and I can see you don't really know what you're talking about. I was incorrect in my assumption also. a lot of the stuff you're babbling about I saw in differential geometry.
although, from what I saw, geometric algebra is just the study of multilinear algebras with certain(convenient) properties, that allow them to be geometrized easier. It's hardly a more general form of linear algebra. All that 'subspaces gunk' comes in very handy when dealing with more advanced stuff.
(btw I still don't see how you get a matrix to jordan form gemoetrically. maybe I'm just stupid)