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Shear mapping. Horizontal shearing of the plane, transforming the blue into the red shape. The black dot is the origin. In fluid dynamics a shear mapping depicts fluid flow between parallel plates in relative motion. In plane geometry, a shear mapping is an affine transformation that displaces each point in a fixed direction by an amount ...
Let X be an affine space over a field k, and V be its associated vector space. An affine transformation is a bijection f from X onto itself that is an affine map; this means that a linear map g from V to V is well defined by the equation () = (); here, as usual, the subtraction of two points denotes the free vector from the second point to the first one, and "well-defined" means that ...
Below is a shear mapping with infinite order. Below that are their compositions, which both have order 3. In mathematics, an iterated function is a function that is obtained by composing another function with itself two or several times. The process of repeatedly applying the same function is called iteration. In this process, starting from ...
The bridge pattern is a design pattern used in software engineering that is meant to "decouple an abstraction from its implementation so that the two can vary independently", introduced by the Gang of Four. [1] The bridge uses encapsulation, aggregation, and can use inheritance to separate responsibilities into different classes.
The mathematical model representing simple shear is a shear mapping restricted to the physical limits. It is an elementary linear transformation represented by a matrix. The model may represent laminar flow velocity at varying depths of a long channel with constant cross-section. Limited shear deformation is also used in vibration control, for ...
Transformation matrix. Central object in linear algebra; mapping vectors to vectors. In linear algebra, linear transformations can be represented by matrices. If is a linear transformation mapping to and is a column vector with entries, then for some matrix , called the transformation matrix of . [citation needed]
Next up on the Dodgers' October conquest: the New York Mets, who will travel to Dodger Stadium for the start of a best-of-seven NL Championship Series on Sunday. First pitch is at 5:15 p.m ...
In this shear mapping the red arrow changes direction, but the blue arrow does not. The blue arrow is an eigenvector of this shear mapping because it does not change direction, and since its length is unchanged, its eigenvalue is 1. A 2×2 real and symmetric matrix representing a stretching and shearing of the plane.