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Bivector

Bivector Bi*vec"tor, n. [Pref. bi- + vector.] (Math.) A term made up of the two parts ? + ?1 ?-1, where ? and ?1 are vectors.

Bivector Bi*vec"tor, n. [Pref. bi- + vector.] (Math.) A term made up of the two parts ? + ?1 ?-1, where ? and ?1 are vectors.

- 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 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...

- 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...

- 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...

- 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...

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

- 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...

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

- 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...

- 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}...

- 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...

- 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...

- 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...

- 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...

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

- 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...

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

- 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...

- 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}...

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