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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.
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 (antenna), the state of polarization (in the above sense) of electromagnetic waves transmitted by or received by a radio antenna; Dielectric polarization, charge separation in insulating materials: Polarization density, volume dielectric polarization; Dipolar polarization, orientation of permanent dipoles
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 ...
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 ...
This is a list of important publications in mathematics, organized by field. Some reasons a particular publication might be regarded as important: Topic creator – A publication that created a new topic; Breakthrough – A publication that changed scientific knowledge significantly
“It’s a kind of backstop for meaning in an era of fake news, alternative facts, whatever you want to say about the value of a word’s meaning in the culture.” It’s notable that “polarization” originated in the early 1800s — and not during the Renaissance, as did most words with Latin roots about science, Sokolowski said.
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 ...