exterior product

Definitions

A kind of product between vectors and/or multivectors which is associative, linear, and alternating.

Examples

“The exterior product of two vectors is a bivector.”

“The exterior product between two vectors is anti-commutative; therefore the exterior product between a vector and itself is zero.”

“The exterior product between a multivector of grade k and a multivector of grade n is a multivector of grade k+n, unless k+n is larger than the dimension of the vector space to which the vectors belong⟳ (out of which the multivectors are constructed), in which case their product is zero.”

“The exterior product between a multivector of grade k and a multivector of grade n is commutative if k times n is even and anti-commutative if k times n is odd. (This is related to what is meant when it is said that the exterior product is alternating. It means that a permutation of the factors of a wedge product of vectors changes the sign⟳ of the product if and only if the permutation is odd.)”

CEFR level