From help-octave-request at bevo dot che dot wisc dot edu Wed Jan 10 07:12:09 2001 Subject: question on vector product From: Rolf Fabian To: "'help-octave UWISC'" Date: Wed, 10 Jan 2001 14:08:35 +0100 Hi I've some general (more or less academical) question concerning the possibility to define a cross -product in N-dim vector spaces. Below, there's an excerpt from Encyclop. Britannica I've found in the net which's related to the topic. Vector Products ......... Unlike the concept of scalar product, the existence of a vector product having the properties listed above depends critically upon the dimension n of the vector space on which it is defined. Except for the trivial cases (n = 0 and n = 1), such a vector product exists only for n = 3 and n= 7. This odd fact is closely related to long-standing problems in algebra, originating in the work of Hamilton and Cayley but only fully solved in the 1960s. Now my questions 1) What's the vector (cross) prod in dimensions n=0,1 2) What's magic with dimension n=7 ? Can anybody give a formulae or describe an algorithm to calculate the7-dim vector (cross) product? Furthermore a question not related to referenced article: 3) Even for (standard) 3-dim space, I've only found definitions for a vector (cross) product defined in Euklidian 3d space (real vectors only). What's the correct definition in unitary 3D-space (complex vectors) ? If any .. are there more than one possibilities for such a definition ? Thanks Rolf ------------------------------------------------------------- Octave is freely available under the terms of the GNU GPL. Octave's home on the web: http://www.octave.org How to fund new projects: http://www.octave.org/funding.html Subscription information: http://www.octave.org/archive.html -------------------------------------------------------------