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English: Three diagrams illustrating divergence of a vector field. The lefthand diagram has positive divergence since the partial derivatives of the field with respect to the and axes are positive. The center diagram has negative divergence since the partial derivatives are negative.
In vector calculus, divergence is a vector operator that operates on a vector field, producing a scalar field giving the quantity of the vector field's source at each point. More technically, the divergence represents the volume density of the outward flux of a vector field from an infinitesimal volume around a given point.
As the name implies, the divergence is a (local) measure of the degree to which vectors in the field diverge. The divergence of a tensor field of non-zero order k is written as =, a contraction of a tensor field of order k − 1. Specifically, the divergence of a vector is a scalar.
The concomitant presence of the lines that end and begin preserves the divergence-free character of the field in the point. [ 5 ] Note that for this kind of drawing, where the field-line density is intended to be proportional to the field magnitude, it is important to represent all three dimensions.
The dual divergence to a Bregman divergence is the divergence generated by the convex conjugate F * of the Bregman generator of the original divergence. For example, for the squared Euclidean distance, the generator is x 2 {\displaystyle x^{2}} , while for the relative entropy the generator is the negative entropy x log x ...
Correct misinterpretations of free images. One of the main complaints about free images is lack of quality when compared with a promotional images. That is not true: there are very good free images as shown by Wikipedia:Featured pictures. In the case of replaceable images, it is possible that a promotional image will look better than free versions.
The optical power directly relates to how large positive images will be magnified, and how small negative images will be diminished. All light sources produce some degree of divergence, as the waves exiting these sources always have some degree of curvature.
Numerous references to earlier uses of the symmetrized divergence and to other statistical distances are given in Kullback (1959, pp. 6–7, §1.3 Divergence). The asymmetric "directed divergence" has come to be known as the Kullback–Leibler divergence, while the symmetrized "divergence" is now referred to as the Jeffreys divergence.