| | 70 | For step (4), perhaps see [http://en.wikipedia.org/wiki/Gram–Schmidt_process Gram-Schmidt process], and also this exchange from the [http://tunes.org/~nef/logs/haskell/10.09.30 #haskell IRC channel on 30 Sep 2010]: |
| | 71 | |
| | 72 | {{{ |
| | 73 | 18:18:27 <byorgey> given a vector v in an inner product space, how might I go about computing a basis for the hyperplane orthogonal to v? |
| | 74 | 18:18:45 <Veinor> ask #math? :D |
| | 75 | 18:19:02 --- join: dnolen (~davidnole@cpe-68-173-254-181.nyc.res.rr.com) joined #haskell |
| | 76 | 18:19:09 * byorgey shudders |
| | 77 | 18:19:11 <ddarius> byorgey: for all basis vectors b, keep b if b ^ v /= 0 |
| | 78 | 18:20:00 --- join: c_wraith (~c_wraith@209.237.247.90) joined #haskell |
| | 79 | 18:20:01 <byorgey> ddarius: ^ is inner product? |
| | 80 | 18:20:10 <Cale> byorgey: Well, pick random vectors and subtract off the orthogonal projection onto the subspace spanned by v |
| | 81 | 18:20:11 <benmachine> isn't ^ usually used for cross product |
| | 82 | 18:20:11 <ddarius> byorgey: Wedge product. |
| | 83 | 18:20:13 <benmachine> or is that v |
| | 84 | 18:20:24 * benmachine always just used, you know, cross |
| | 85 | 18:20:30 <ddarius> Of course, the dual of v will be a blade that represents the hyperplane orthogonal to it already... |
| | 86 | 18:20:50 <aristid> so google found IOSpec for me http://www.cse.chalmers.se/~wouter/repos/IOSpec/index.html |
| | 87 | 18:20:53 <ddarius> b ^ v = b . dual(v) |
| | 88 | 18:21:08 <byorgey> ddarius: where can I read about this? |
| | 89 | 18:21:28 <Veinor> byorgey: for each basis vector b, compute b - proj_v b |
| | 90 | 18:21:36 <byorgey> can I apply affine transformations to such duals? |
| | 91 | 18:21:47 <Veinor> (I don't know anything about vector spaces besides R^n) |
| | 92 | 18:22:42 <ddarius> http://geocalc.clas.asu.edu/ (mathematical/physics), http://www.mrao.cam.ac.uk/~clifford/ (physics), http://www.science.uva.nl/ga/ (computer science) |
| | 93 | 18:22:47 <ddarius> byorgey: ^ |
| | 94 | 18:23:36 <benmachine> haskell-src-exts' fixity resolution is super-brokwn |
| | 95 | 18:23:39 <benmachine> *broken |
| | 96 | 18:23:45 <benmachine> well, fairly broken anyway |
| | 97 | 18:24:12 <ddarius> byorgey: I recommend starting here: http://geocalc.clas.asu.edu/html/Intro.html and here: http://www.science.uva.nl/ga/publications/index.html |
| | 98 | 18:25:14 <ddarius> byorgey: This deceptively named paper is rather useful a bit later on: http://www.science.uva.nl/ga/publications/content_publications.html#leo_inner |
| | 99 | }}} |
| | 100 | |
