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...
67 KB (9,905 words) - 13:15, 29 August 2024
Poisson manifold (redirect from Poisson bivector)
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...
61 KB (9,227 words) - 13:51, 23 July 2024
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...
8 KB (926 words) - 01:16, 22 October 2022
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...
14 KB (2,020 words) - 00:58, 17 April 2024
Plane of rotation (section Bivectors)
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...
24 KB (3,575 words) - 21:13, 20 August 2023
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...
29 KB (4,144 words) - 04:30, 3 September 2024
Electromagnetic tensor (redirect from Maxwell bivector)
(sometimes called the field strength tensor, Faraday tensor or Maxwell bivector) is a mathematical object that describes the electromagnetic field in spacetime...
16 KB (2,787 words) - 00:47, 31 July 2024
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...
33 KB (7,290 words) - 00:00, 27 July 2024
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}...
4 KB (633 words) - 19:05, 4 March 2024
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...
75 KB (11,475 words) - 18:39, 5 September 2024