
#1
May2507, 03:41 AM

P: 185

Why is it possible to take the cross product in only 3 and 7 dimensions?




#2
May2507, 04:14 AM

Emeritus
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PF Gold
P: 16,101

Er, could you clarify the question?
Although I don't know precisely what you're asking, I suspect the answer has to do with the Quaternions and Octonions. 



#3
May2507, 04:34 AM

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HW Helper
P: 9,398

If you mean 'why do their exist antisymmetric linear pairings x/\y : R^nxR^n>R^n for some n, and not others', then Hurkyl is getting there. There is a theorem in differential geometry that explains this, though I don't know what it is saying (i.e. I can't encapsulate it into a nice bite sized slogan for the lay person).




#4
May2507, 07:33 PM

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P: 9,428

Cross Product
existence of pairings produces vector fields on the sphere, and these exist only in a few cases. maybe this is related.



#5
May2707, 04:40 PM

P: n/a

Well, the idea is that a matrix is created. The determinent can do very funny things. Just try to find the determinents of 3x3, 4x4, 5x5, 6x6, 7x7. You may figure out why...




#6
May2707, 06:49 PM

P: 185

OK. Thanks




#7
May2807, 04:03 AM

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P: 9,398




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