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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
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 ...
In representation theory, polarization is the maximal totally isotropic subspace of a certain skew-symmetric bilinear form on a Lie algebra.The notion of polarization plays an important role in construction of irreducible unitary representations of some classes of Lie groups by means of the orbit method [1] as well as in harmonic analysis on Lie groups and mathematical physics.
In mathematics, the Jacobian variety J(C) of a non-singular algebraic curve C of genus g is the moduli space of degree 0 line bundles. It is the connected component of the identity in the Picard group of C , hence an abelian variety .
In addition to polarization, other words on the list include totality, demure, pander, resonate and more. Merriam-Webster's word of the year is polarization: See more words that defined 2024 Skip ...
“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.