- Inverse (mathematics)
Inverse is the opposite of something. This word and its derivatives are used greatly 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,
**theadditive inverse of "x" is –"x";
**themultiplicative inverse 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 ,
**inverse kinematics ,
**inverse dynamics .
* Inverse perspective — the further the objects, the larger they are drawn.
*Inversive ring geometry — classical projective geometry extended by ring theory
*Inverse-square law — the magnitude of a force is proportional to the inverse square of the distance.
*Inverse transform sampling method — 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
Wikimedia Foundation. 2010.