Talk:Seven-dimensional cross product: Difference between revisions
Eebster the Great (talk | contribs) No edit summary |
86.80.122.213 (talk) No edit summary |
||
| Line 2: | Line 2: | ||
Why can't cross products be defined in fifteen dimensions? The article should provide at least some explanation, even if it's obvious, because nothing's really obvious at this level. [[User:Eebster the Great|Eebster the Great]] ([[User talk:Eebster the Great|talk]]) 02:36, 8 December 2008 (UTC) |
Why can't cross products be defined in fifteen dimensions? The article should provide at least some explanation, even if it's obvious, because nothing's really obvious at this level. [[User:Eebster the Great|Eebster the Great]] ([[User talk:Eebster the Great|talk]]) 02:36, 8 December 2008 (UTC) |
||
I've read the attached reference to Multi-dimensional vector product by Z.K.Silagadze. The quote of interest would be: |
|||
"From a view point of composition algebra,the vector product is just the commutator divided by two. According to Hurwitz theorem the only composition algebras are real numbers,complex numbers,quaternions and Octonions. Quaternions produce the usual three-dimensional vector products. The seven-dimensional vector product is generated by Octonions." |
|||
I'll try to put this in with a tag for improvement. |
|||
Revision as of 00:01, 3 April 2009
Is this an Exterior product or something else? --Salix (talk): 19:19, 27 September 2008 (UTC)
Why can't cross products be defined in fifteen dimensions? The article should provide at least some explanation, even if it's obvious, because nothing's really obvious at this level. Eebster the Great (talk) 02:36, 8 December 2008 (UTC)
I've read the attached reference to Multi-dimensional vector product by Z.K.Silagadze. The quote of interest would be: "From a view point of composition algebra,the vector product is just the commutator divided by two. According to Hurwitz theorem the only composition algebras are real numbers,complex numbers,quaternions and Octonions. Quaternions produce the usual three-dimensional vector products. The seven-dimensional vector product is generated by Octonions." I'll try to put this in with a tag for improvement.