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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 ...
An example of a non-linear reading path might be a text that has images alongside it. Kress argues that this different mode yields a different affordance; the visual image allows for open interpretation. A concrete example on paper might be a diagram such as a flow chart or graphic organizers. In such multi-modal texts, the reading path is much ...
In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry.As Euclidean geometry lies at the intersection of metric geometry and affine geometry, non-Euclidean geometry arises by either replacing the parallel postulate with an alternative, or relaxing the metric requirement.
In mathematics and science, a nonlinear system (or a non-linear system) is a system in which the change of the output is not proportional to the change of the input. [1] [2] Nonlinear problems are of interest to engineers, biologists, [3] [4] [5] physicists, [6] [7] mathematicians, and many other scientists since most systems are inherently nonlinear in nature. [8]
Similarly, S′ is the perceived linear extent by which the subjective point A′ appears directly above point B′. The observer could simply say how many inches or meters that vertical distance looks. For a viewed object, S′ thus is its perceived linear size in meters, (or apparent linear size).
The sine of the angles between subspaces satisfy the triangle inequality in terms of majorization and thus can be used to define a distance on the set of all subspaces turning the set into a metric space. [6] For example, the sine of the largest angle is known as a gap between subspaces. [9]
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A quadrilateral such as BCEF is called an adventitious quadrangle when the angles between its diagonals and sides are all rational angles, angles that give rational numbers when measured in degrees or other units for which the whole circle is a rational number. Numerous adventitious quadrangles beyond the one appearing in Langley's puzzle have ...