Fixed point (mathematics)
In mathematics, a fixed point (sometimes shortened to fixpoint, also known as an invariant point) of a function is an element of the function's domain that is mapped to itself by the function.
Description
Not all functions have fixed points: for example, if f is a function defined on the real numbers as f(x) = x + 1, then it has no fixed points, since x is never equal to x + 1 for any real number.
In graphical terms, a fixed point means the point (x, f(x)) is on the line y = x, or in other words the graph of f has a point in common with that line.
Points that come back to the same value after a finite number of iterations of the function are called periodic points.
A fixed point is a periodic point with period equal to one.
In projective geometry, a fixed point of a projectivity has been called a double point.
In Galois theory, the set of the fixed points of a set of field automorphisms is a field called the fixed-point subring of the set of automorphisms.
See also
- Eigenvector
- Equilibrium
- Fixed-point combinator
- Fixed-point subgroup
- Fixed-point subring
- Fixed-point theorems
- Fixed points of a Möbius transformation
- Function (mathematics)
- Idempotent
- Infinite compositions of analytic functions
- Invariant (mathematics)
- Map (mathematics)
- Periodic point
External links
- Fixed point (mathematics) @ Wikipedia
