Re: Outer product in mathematica
- To: mathgroup at smc.vnet.net
- Subject: [mg51282] Re: [mg51261] Outer product in mathematica
- From: Matteo Delfino <delfino at studenti.ph.unito.it>
- Date: Tue, 12 Oct 2004 01:57:45 -0400 (EDT)
- References: <200410110525.BAA05003@smc.vnet.net>
- Reply-to: delfino at studenti.ph.unito.it
- Sender: owner-wri-mathgroup at wolfram.com
Jonas Sourlier ha scritto: > Hi there > > In the lections at my University I have learnt that the outer product > of two Vectors is defined as follows: > > (a) x (b) = 0 > (a, b) x (c, d) = ad - bc > (a, b, c) x (d, e, f) = (bf - ce, cd - af, ae - bd) > > For two four-dimensional Vectors the outer product produces a > six-dimensional Vector (handled as a skew-symmetric 4x4-matrix). > The general, axiomatic definition of the outer product says that it is > > graduately anti-commutative: u x v = (-1)^(k+l) (v x u) > bilinear: (u + v) x w = u x w + v x w > > for two vectors u, v and w with dimensions k, l, m. > > > Now, my question: The outer product seems to be implemented in > Mathematica with the function Outer. But whatever I've tried so far > with Outer I didn't manage to get the outer product of two vectors as > described above. > > Outer[Times, {a,b,c},{d,e,f}] produces the 3x3-Matrix > > {{a d, a e, a f}, {b d, b e, b f}, {c d, c e, c f}} > > How can I calculate the outer product of two vectors with Mathematica? > > Thank a lot for helping me! > Jonas Outer product (or tensor product) and cross product are not the same thing.Outer product is defined between two tensors and produces a tesor of higher rank,cross product takes two vector (read:tensor of the same rank) and produces another vector (read:tensor of the same rank as before).In mathematica cross product is defined as Cross[] and Outer product as Outer[]. YOU MUST USE CROSS[]. DEFINITION OF CROSS PRODUCT BY OUTER PRODUCT It is still possible to extend the definition of Cross[] product to tensors of any rank,try searching google for informations such as: http://www.math.wisc.edu/~milewski/321f04/fwnotestensors.pdf http://groups.google.it/groups?q=%22tensor+product%22+%22cross+product%22&hl=it&lr=&selm=gAnda.419%24DS2.99500%40newsfep1-win.server.ntli.net&rnum=1 Hope It helps. Delfino Matteo
- References:
- Outer product in mathematica
- From: Jonas Sourlier <aeroswiss@gmx.ch>
- Outer product in mathematica