bivector
Sign in to savethumb|170px|Parallel plane segments with the same orientation and area corresponding to the same bivector .
Article
34 sectionsContents
- History
- Derivation
- Geometric algebra and the geometric product
- Scalar product
- Exterior product
- Properties
- The space ⋀<sup>2</sup>R<sup>''n''</sup>
- Even subalgebra
- Magnitude
- Unit bivectors
- Simple bivectors
- Product of two bivectors
- General bivectors and matrices
- Two dimensions
- Complex numbers
- Three dimensions
- Quaternions
- Rotation vector
- Rotors
- Axial vectors
- Geometric interpretation
- Four dimensions
- Orthogonality
- Simple bivectors in 4D
- Rotations in R<sup>4</sup>
- Spacetime rotations
- Maxwell's equations
- Higher dimensions
- Rotations in higher dimensions
- Projective geometry
- Tensors and matrices
- See also
- Notes
- General references
thumb|170px|Parallel plane segments with the same orientation and area corresponding to the same bivector .
In mathematics, a bivector or 2-vector is a quantity in exterior algebra or geometric algebra that extends the idea of scalars and vectors. Considering a scalar as a degree-zero quantity and a vector as a degree-one quantity, a bivector is of degree 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 vector quaternions in three dimensions. They can be used to generate rotations in a space of any number of dimensions, and are a useful tool for classifying such rotations.