|
In [[mathematics]], a '''transition function''' hasmay severalrefer different meaningsto:
* a [[transition map]] between two charts of an atlas of a manifold or other topological space
* the function that defines the transitions of a [[transition system]] in computing, which may refer more specifically to a
** [[Turing machine]],
** [[finite-state machine]], or
** [[cellular automaton]]
* Ina [[ statisticsstochastic kernel]] In statistics and [[probability theory ]], a '''transition function''' is a [[stochastic kernel]], the [[conditional probability distribution ]] function controlling the transitions of a [[stochastic process ]].▼
== See also ==
* In [[topology]], a '''transition function''' is a [[homeomorphism]] from one coordinate [[Atlas (topology)|chart]] to another. Given two charts (''U''<sub>''i''</sub>, φ<sub>''i''</sub>) and (''U''<sub>''j''</sub>, φ<sub>''j''</sub>) a transition [[function (mathematics)|function]] normally takes the form
* [[Non-analytic smooth function#Smooth transition functions]]
::<math>\phi_i\phi_j^{-1} : (U_i \cap U_j) \times F \to (U_i \cap U_j) \times F</math>
:for some [[Set (mathematics)|set]] ''F'' being covered by the [[topology]]. See [[fiber bundle]], in particular also [[Vector_bundle#Transition_functions|vector bundle]], and [[atlas (topology)]] for additional details.
{{mathdab}}
* In [[computing]], a '''transition function''' is the function that defines the state transitions of a [[Turing machine]], [[finite-state machine]], or [[cellular automaton]].
▲* In [[statistics]] and [[probability theory]], a '''transition function''' is a [[stochastic kernel]], the [[conditional probability distribution]] function controlling the transitions of a [[stochastic process]].
{{mathdab}}[[Category:Homeomorphisms]]
[[es:Función de transición]]
[[pt:Função de transição]]
[[sk:Prechodová funkcia]]
[[zh:轉換函數]]
| 