Bivectors - Binors - 2-vectors
- is a quantity in exterior algebra or geometric algebra that extends the idea of scalars and vectors
- is a type of k-vector where k=2
- Today the bivector is largely studied as a topic in geometric algebra, a Clifford algebra over real or complex vector spaces with a quadratic form
- just as the standard basis vectors are formed by unit vectors, so is the standard basis bivectors are formed by unit planes
- just as 1-vectors are projections of a position in space onto the basis vectors, so are 2-vectors projections of an area in space onto basis bivectors
- does NOT encode position in the associated vector space
- When we take the wedge product of 2 vectors result is, 𝐮∧𝐯 = (𝑢1𝑣1+ 𝑢2𝑣2)(𝐞1∧𝐞2)
- scalar part is the area of the parallelepiped (i.e. 𝑢1𝑣1+ 𝑢2𝑣2)
- bivector part is the “direction” of that area (i.e. 𝐞1∧𝐞2)