7 dimensional cross product

7 dimensional cross product

Why 3 and 7 ? I know from some reading that Hurwitz's Theorem explains this, but can someone help me build some intuition behind this or.
Nonzero binary cross products exist only in three and seven dimensions. Further products are possible when lifting the restriction that it  ‎ Multiplication table · ‎ Definition · ‎ Consequences of the defining.
I've always heard that the cross product only exists in a well defined way for 3 and 7 dimensions. From my own reading I've found that a cross  Wedge vs cross products.

7 dimensional cross product - phone

In attempting to find out how to manipulate three-tuples like we currently play with vectors, a mathematician named Hamilton invented quaternion s. Learn more about hiring developers or posting ads with us. However, math is very curious in its allowances of the absurd. Show Ignored Content Know someone interested in this topic? The week's top questions and answers. If you're willing to give up associativity as well, but want to keep one other more technical property, you get a fourth and final algebra: an eight-dimensional object called the octonians. I've always called it the cross product. However, there exists 7 dimensional cross product quirk of mathematics that allows for a simplification down to two inputs. Similar Discussions: Higher dimensional cross products. You can never become anything if you're not good at math. Representations and Why Precision is Important. Anybody can ask a question. 7 dimensional cross product