Simple rotations are generated by simple bivectors, with the fixed plane the dual or orthogonal to the plane of the bivector.
32.
We will use the symbol " F " to denote either the bivector or the operator, according to context.
33.
The set of all such tensors-often called bivectors-forms a vector space of dimension 6, sometimes called bivector space.
34.
The product of the bivector with a complex number on the unit circle is then called an " elliptical rotation ".
35.
In particular the exponent of a bivector associated with a rotation is a rotation matrix, that is the rotation matrix " M"
36.
In other dimensions there are vector-valued products of three or more vectors that satisfy these conditions, and binary products with bivector results.
37.
Notice that because " V " has dimension two the basis bivector is the only multivector in ? " V ".
38.
In three dimensions bivectors are dual to vectors so the product is equivalent to the cross product, with the bivector instead of its vector dual.
39.
In this context of geometric algebra, this bivector is called a pseudovector, and is the " dual " of the cross product.
40.
Physical quantities such as angular momentum which can be identified with the magnitude of a bivector have the geometric dimension of " area ".
