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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 diagonal.
Polarization of an Abelian variety, in the mathematics of complex manifolds Polarization of an algebraic form , a technique for expressing a homogeneous polynomial in a simpler fashion by adjoining more variables
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 ...
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 ...
Equivalently, we have to specify the dependence of the polarization P (hence the bound charge) and the magnetization M (hence the bound current) on the applied electric and magnetic field. The equations specifying this response are called constitutive relations. For real-world materials, the constitutive relations are rarely simple, except ...
The Jones vector describes the polarization of light in free space or another homogeneous isotropic non-attenuating medium, where the light can be properly described as transverse waves. Suppose that a monochromatic plane wave of light is travelling in the positive z -direction, with angular frequency ω and wave vector k = (0,0, k ), where the ...
“Polarization means that we are tending toward the extremes rather than toward the center.” The election was so divisive, many American voters went to the polls with a feeling that the opposing candidate was an existential threat to the nation.
Physical optics is used to explain effects such as diffraction. In physics, physical optics, or wave optics, is the branch of optics that studies interference, diffraction, polarization, and other phenomena for which the ray approximation of geometric optics is not valid.