exterior product
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English[edit]
Noun[edit]
exterior product (plural exterior products)
- (algebra) A kind of product between vectors and/or multivectors which is associative, linear, and alternating.
- 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.)
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Further reading[edit]
Exterior algebra on Wikipedia.Wikipedia - Multivector on Wikipedia.Wikipedia
