Multivector
![Orientation defined by an ordered set of vectors.Reversed orientation corresponds to negating the exterior product.Geometric interpretation of grade n elements in a real exterior algebra for n = 0 (signed point), 1 (directed line segment, or vector), 2 (oriented plane element), 3 (oriented volume). The exterior product of n vectors can be visualized as any n-dimensional shape (e.g. n-parallelotope, n-ellipsoid); with magnitude (hypervolume), and orientation defined by that on its (n − 1)-dimensional boundary and on which side the interior is.[19][20]](/Images/godic/202501/28/N_vector_positive_png_version3918.png")
![](/Images/godic/202501/28/N_vector_negative_png_version3918.png")
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.