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...

bracket of the coordinate functions. A Poisson bivector on a smooth manifold M {\displaystyle M} is a bivector field π ∈ X 2 ( M ) := Γ ( ∧ 2 T M ) {\displaystyle...

a bivector is the vector part of a biquaternion. For biquaternion q = w + xi + yj + zk, w is called the biscalar and xi + yj + zk is its bivector part...

six-dimensional bivectors in four dimensions. These can be written Λ 2 R 4 {\displaystyle \Lambda ^{2}\mathbb {R} ^{4}} for the set of bivectors in Euclidean...

geometric algebra, with the planes of rotations associated with simple bivectors in the algebra. Planes of rotation are not used much in two and three...

number) part and a bivector part. (A scalar is a quantity with no orientation, a vector is a quantity oriented like a line, and a bivector is a quantity oriented...

(sometimes called the field strength tensor, Faraday tensor or Maxwell bivector) is a mathematical object that describes the electromagnetic field in spacetime...

graded multivectors: scalars are grade 0, usual vectors are grade 1, bivectors are grade 2 and the highest grade (3 in the 3D case) is traditionally...

or wedge product – a binary operation on two vectors that results in a bivector. In Euclidean 3-space, the wedge product a ∧ b {\displaystyle \mathbf {a}...

of a bivector and vector. In three dimensions bivectors are dual to vectors so the product is equivalent to the cross product, with the bivector instead...