- Inverse (mathematics)
**Inverse**is the opposite of something. This word and its derivatives are used greatly inmathematics , 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.*

### Look at other dictionaries:

**Inverse**— or inversion may refer to:* Inverse (program), a program for solving inverse and optimization problems * Inversion (music) * Inversion (prosody), the reversal of the order of a foot s elements * Inversion (linguistics) * Inversion (law),… … Wikipedia**Inverse (program)**— Inverse is a general purpose computer program for solving inverse and optimization problems. The program has been designed in particular for solving problems where complex numerical simulations (e.g. by the finite element method) are involved in… … Wikipedia**Inverse transform sampling**— Inverse transform sampling, also known as the probability integral transform, is a method of generating sample numbers at random from any probability distribution given its cumulative distribution function (cdf). This method is generally… … Wikipedia**inverse**— ► ADJECTIVE ▪ opposite in position, direction, order, or effect. ► NOUN 1) a thing that is the opposite or reverse of another. 2) Mathematics a reciprocal quantity. DERIVATIVES inversely adverb. ORIGIN Latin inversus, from invertere … English terms dictionary**mathematics**— /math euh mat iks/, n. 1. (used with a sing. v.) the systematic treatment of magnitude, relationships between figures and forms, and relations between quantities expressed symbolically. 2. (used with a sing. or pl. v.) mathematical procedures,… … Universalium**Inverse function**— In mathematics, if fnof; is a function from A to B then an inverse function for fnof; is a function in the opposite direction, from B to A , with the property that a round trip (a composition) from A to B to A (or from B to A to B ) returns each… … Wikipedia**Inverse limit**— In mathematics, the inverse limit (also called the projective limit) is a construction which allows one to glue together several related objects, the precise manner of the gluing process being specified by morphisms between the objects. Inverse… … Wikipedia**Inverse function theorem**— In mathematics, specifically differential calculus, the inverse function theorem gives sufficient conditions for a function to be invertible in a neighborhood of a point in its domain. The theorem also gives a formula for the derivative of the… … Wikipedia**Inverse relation**— In mathematics, the inverse relation of a binary relation is the relation that occurs when you switch the order of the elements in the relation. For example, the inverse of the relation child of is the relation parent of . In formal… … Wikipedia**Inverse problem**— An inverse problem is a general framework that is used to convert observed measurements into information about a physical object or system that we are interested in. For example, if we have measurements of the Earth s gravity field, then we might … Wikipedia