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
- Inverse problem — the task of identifying model parameters from observed data; see for example
- 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.
- In set theory, the inverse of a set is called Complement (set theory).
