How come the cross product is only well-defined in 3 dimensions or 7 dimensions? What's up with that?
What have you tried, dear frogposter?
>>16806766I've tried asking on 4chan. Is there an intuitive reason why this should only work in dimensions 3 and 7?
>>16807443What do you mean by "this"? I don't know how you would generalize the formula for cross product to higher dimensions
>>16807443It also works in dimensions 1 and 0, because powers of 2.
>>16806690Since the only normed division algebras are the quaternions and the octonions, the cross product is formed from the product of the normed division algebra by restricting it to the 0,1,3,7 imaginary dimensions of the algebra. This gives nonzero products in only three and seven dimensions.
>>16806690Check out this, especially at 27:16https://www.youtube.com/watch?v=60z_hpEAtD8
