What is "multivector"

n. (context mathematics English) An element of a particular type of vector space

A multivector is the result of a product defined for elements in a vector space V. A vector space with a linear product operation between elements of the space is called an algebra; examples are matrix algebra and vector algebra. The algebra of multivectors is constructed using the wedge product ∧ and is related to the exterior algebra of differential forms.

The set of multivectors on a vector space V is graded by the number of basis vectors that form a basis multivector. A multivector that is the product of p basis vectors is called a grade p multivector, or a p-vector. The linear combination of basis p-vectors forms a vector space denoted as Λ(V). The maximum grade of a multivector is the dimension of the vector space V.

The product of a p-vector and a k-vector is a -vector so the set of linear combinations of all multivectors on V is an associative algebra, which is closed with respect to the wedge product. This algebra, denoted by Λ(V), is called the exterior algebra of V.