Multivector
From Wikipedia, the free encyclopedia
In a Grassmann algebra, a multivector is an element of a vector space V. A k-multivector is a k-fold product
where 
denotes wedge product and the k-th exterior power,
- Λk(V),
is the vector space of formal sums of k-multivectors. The product of a k-multivector and an 
-multivector is a 
-multivector. So, the direct sum 
forms an associative algebra, which is closed with respect to the wedge product. This algebra, commonly denoted by Λ(V), is called the exterior algebra of V.
In geometric algebra, multivectors are defined to be summations of such k-blades such as the summation of a scalar, a vector, a 2-vector.
