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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 ...
Defined as a “division into two sharply distinct opposites,” “polarization” grew dramatically in search volume over the past year due to what the online dictionary site claims was the ...
Polarization is an important parameter in areas of science dealing with transverse waves, such as optics, seismology, radio, and microwaves. Especially impacted are technologies such as lasers, wireless and optical fiber telecommunications, and radar.
“The basic job of the dictionary is to tell the truth about words,” the Merriam-Webster editor continued. “We’ve had dictionaries of English for 420 years and it’s only been in the last 20 years or so that we’ve actually known which words people look up.” “Polarization” extends beyond political connotations.
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.