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In mathematics, in particular in algebra, polarization is a technique for expressing a homogeneous polynomial in a simpler fashion by adjoining more variables. Specifically, given a homogeneous polynomial, polarization produces a unique symmetric multilinear form from which the original polynomial can be recovered by evaluating along a certain ...
In linear algebra, a branch of mathematics, the polarization identity is any one of a family of formulas that express the inner product of two vectors in terms of the norm of a normed vector space. If a norm arises from an inner product then the polarization identity can be used to express this inner product entirely in terms of the norm. The ...
Polarization (physics), the ability of waves to oscillate in more than one direction; polarization of light allows the glare-reducing effect of polarized sunglasses Polarization (antenna) , the state of polarization (in the above sense) of electromagnetic waves transmitted by or received by a radio antenna
The next step in the process of geometric quantization is the choice of a polarization. A polarization is a choice at each point in a Lagrangian subspace of the complexified tangent space of . The subspaces should form an integrable distribution, meaning that the commutator of two vector fields lying in the subspace at each point should also ...
The Jones matrix for an arbitrary birefringent material is the most general form of a polarization transformation in the Jones calculus; it can represent any polarization transformation. To see this, one can show
See polarization and plane of polarization for more information. The orientation of a linearly polarized electromagnetic wave is defined by the direction of the electric field vector. [ 2 ] For example, if the electric field vector is vertical (alternately up and down as the wave travels) the radiation is said to be vertically polarized.
Animosity between partisan voters has grown in recent years. Gutzemberg/Shutterstock.comPoliticians and pundits from all quarters often lament democracy’s polarized condition. Similarly ...
In electrodynamics, circular polarization of an electromagnetic wave is a polarization state in which, at each point, the electromagnetic field of the wave has a constant magnitude and is rotating at a constant rate in a plane perpendicular to the direction of the wave.