exterior algebra

In mathematics, the exterior algebra of a vector space is a graded associative algebra Elements in ∧nV are called -multivectors, and are given by a sum of -blades ("products" of elements of ); it is an abstraction of oriented lengths, areas, volumes and more generally oriented n-volumes for n ≥ 0. The algebra product ∧ on ∧V is called the exterior product or wedge product; informally, it acts by taking the product of oriented volumes. Every element in ∧V is a sum of v1∧ ... ∧ vk where , and Such an element is called a k-blade, which in the above figure corresponds to the parallelotope spanned by them.