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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 ...
the bivector has two distinct principal null directions; in this case, the bivector is called non-null. Furthermore, for any non-null bivector, the two eigenvalues associated with the two distinct principal null directions have the same magnitude but opposite sign, λ = ±ν, so we have three subclasses of non-null bivectors: spacelike: ν = 0
conserved, bivector Angular velocity: ω: The angle incremented in a plane by a segment connecting an object and a reference point per unit time rad/s T −1: bivector Area: A: Extent of a surface m 2: L 2: extensive, bivector or scalar Centrifugal force: F c: Inertial force that appears to act on all objects when viewed in a rotating frame of ...
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 ...
The most common description of the electromagnetic field uses two three-dimensional vector fields called the electric field and the magnetic field.These vector fields each have a value defined at every point of space and time and are thus often regarded as functions of the space and time coordinates.
This theory stipulated that all the laws of physics should take the same form in all coordinate systems – this led to the introduction of tensors. The tensor formalism also leads to a mathematically simpler presentation of physical laws. The inhomogeneous Maxwell equation leads to the continuity equation:
Examples of geometric algebras applied in physics include the spacetime algebra (and the less common algebra of physical space). Geometric calculus , an extension of GA that incorporates differentiation and integration , can be used to formulate other theories such as complex analysis and differential geometry , e.g. by using the Clifford ...
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:
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