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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 (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
Crystallography is one of the traditional areas of geology that use mathematics. Crystallographers make use of linear algebra by using the Metrical Matrix. The Metrical Matrix uses the basis vectors of the unit cell dimensions to find the volume of a unit cell, d-spacings, the angle between two planes, the angle between atoms, and the bond ...
The azimuth is the angle formed between a reference direction (in this example north) and a line from the observer to a point of interest projected on the same plane as the reference direction orthogonal to the zenith.
The use of degrees is most common in geography, astronomy, and engineering, where radians are commonly used in mathematics and theoretical physics. The unit for radial distance is usually determined by the context, as occurs in applications of the 'unit sphere', see applications .
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 ...
To describe the points which are unmoved by the symmetry operations of the point group, we draw a straight line joining two unmoved points. This line is called a polar direction. The electric polarization must be parallel to a polar direction. In polar point groups of high symmetry, the polar direction can be a unique axis of rotation, but if ...