In
mathematics, a
bivector or
2-vector is a quantity in
exterior algebra or
geometric algebra that extends the idea of
scalars and
vectors. If a scalar is considered an order zero quantity, and a vector is an order one quantity, then a bivector can be thought of as being of order two. Bivectors have applications in many areas of mathematics and physics. They are related to
complex numbers in two dimensions and to both
pseudovectors and
quaternions in three dimensions. They can be used to generate
rotations in any dimension, and are a useful tool for classifying such rotations. They also are used in
physics, tying together a number of otherwise unrelated quantities.