exterior product

== English == === Noun === exterior product (plural exterior products) (algebra) A kind of product between vectors and/or multivectors which is associative, linear, and alternating. 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.) ==== Synonyms ==== Grassmann product ==== Related terms ==== exterior algebra exterior derivative ==== See also ==== wedge product ==== Further reading ==== Exterior algebra on Wikipedia.Wikipedia Multivector on Wikipedia.Wikipedia