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Inverse (mathematics) : ウィキペディア英語版
Inverse (mathematics)


In many contexts in mathematics the term inverse indicates the opposite of something. This word and its derivatives are used widely in mathematics, as illustrated below.

* Inverse element of an element ''x'' with respect to a binary operation
* with identity element ''e'' is an element ''y'' such that ''x''
* ''y'' = ''y''
* ''x'' = ''e''. In particular,
*
* the additive inverse of ''x'' is ''−x'';
*
* the multiplicative inverse or reciprocal of ''x'' is ''x''−1.
*
* inverse function — inverse element with respect to function composition: a function that "reverses" the action of a given function: ''f''−1(''f''(''x'')) = ''x''.
* Inversion in a point — a geometric transform.
* Circle inversion — another particular geometric transformation of a plane that maps the outside of a circle to the inside and vice versa.
* Inverse limit — a notion in abstract algebra.
* Inverse (logic) — ~''p'' → ~''q'' is the inverse of ''p'' → ''q''.
* Inverse matrix — inverse element with respect to matrix multiplication.
* Pseudoinverse, a generalization of the inverse matrix.
* Inverse proportion, also ''inversely proportional'' — a relationship between two variables ''x'' and ''y'' characterized by the equation y=k/x.
* Inverse problem — the task of identifying model parameters from observed data; see for example
*
*inverse scattering problem
*
*inverse kinematics
*
*inverse dynamics.
* Inverse perspective — the further the objects, the larger they are drawn.
*Inverse semigroup
*Inverse of an element in a semigroup
* Inverse-square law — the magnitude of a force is proportional to the inverse square of the distance.
* Inverse transform sampling — generate some random numbers according to a given probability distribution.
* Inverse chain rule method — related to integration and differentiation.
* Inversion of elements, a pair of adjacent out-of-order elements of a permutation (viewed as a list).
* Inverse relation
* Inversion transformation, an extension of Poincaré transformation.
==See also==

* Inversion (disambiguation)

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抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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