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Parallel plane segments with the same orientation and area corresponding to the same bivector a ∧ b. [1] 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 ...
An example of a null field is a plane electromagnetic wave in Minkowski space. A non-null field is characterised by P 2 + Q 2 ≠ 0 {\displaystyle P^{2}+Q^{2}\neq \,0} . If P ≠ 0 = Q {\displaystyle P\neq 0=Q} , there exists an inertial reference frame for which either the electric or magnetic field vanishes.
L 2 T −3: Action: S: Momentum of particle multiplied by distance travelled J/Hz L 2 M T −1: scalar Angular acceleration: ω a: Change in angular velocity per unit time rad/s 2: T −2: Area: A: Extent of a surface m 2: L 2: extensive, bivector or scalar Area density: ρ A: Mass per unit area kg⋅m −2: L −2 M: intensive Capacitance: C ...
The Maharashtra State Board of Secondary and Higher Secondary Education (Abbreviation: MSBSHSE) is a statutory and autonomous body established under the "Maharashtra Secondary Boards Act" 1965 (amended in 1977). [1] Most important task of the board, among few others, is to conduct the SSC for 10th class and HSC for 12th class examinations. [2]
The source free equations can be written by the action of the exterior derivative on this 2-form. But for the equations with source terms (Gauss's law and the Ampère-Maxwell equation), the Hodge dual of this 2-form is needed. The Hodge star operator takes a p-form to a (n − p)-form, where n is the number of dimensions.
The electromagnetic tensor, conventionally labelled F, is defined as the exterior derivative of the electromagnetic four-potential, A, a differential 1-form: [1] [2] = . Therefore, F is a differential 2-form— an antisymmetric rank-2 tensor field—on Minkowski space. In component form,
A two-vector or bivector [1] is a tensor of type () and it is the dual of a two-form, meaning that it is a linear functional which maps two-forms to the real numbers (or more generally, to scalars). The tensor product of a pair of vectors is a two-vector. Then, any two-form can be expressed as a linear combination of tensor products of pairs of ...
A 2-blade is a simple bivector. Sums of 2-blades are also bivectors, but not always simple. A 2-blade may be expressed as the wedge product of two vectors a and b: . A 3-blade is a simple trivector, that is, it may be expressed as the wedge product of three vectors a, b, and c: .