Meanings
plural transition functions
- computingA function from (state, input symbol) to state describing what state to move to on receiving a given input in a given state.
- differential geometryA homeomorphism that bijects between the subsets of the images of two overlapping coordinate charts that are shared in the preimage: For (U_1,φ₁) and (U_2,φ₂) coordinate charts with U_1∩U_2≠∅, the transition functions φ₁₂=φ₂∘φ₁⁻¹ and its inverse φ₂₁=φ₁∘φ₂⁻¹ may be constructed.
1 more example
If (U#95;1,#92;psi#95;1) and (U#95;2,#92;psi#95;2) are two complex charts, then the transition function is #92;psi#95;#123;12#125;#58;#92;psi#95;1(U#95;1#92;capU#95;2)#92;rightarrow#92;psi#95;2(U#95;1#92;capU#95;2), given by #92;psi#95;#123;12#125;#61;#92;psi#95;2#92;circ#92;psi#95;1#123;-1#125;. We say M is a complex manifold if it has an atlas of complex charts (U,#92;psi), such that all the transition functions are holomorphic, as maps from #92;mathbb#123;C#125;ᵐ to itself.
2007, Dominic D. Joyce, Riemannian Holonomy Groups and Calibrated Geometry (Oxford graduate texts in mathematics), Oxford University Press, →ISBN, →LCCN, page 76Synonyms: transition map
Synonyms & antonyms
nounA homeomorphism that bijects between the subsets of the images of two overlapping coordinate charts that are shared in the preimage: For (U_1,φ₁) and (U_2,φ₂) coordinate charts with U_1∩U_2≠∅, the transition functions φ₁₂=φ₂∘φ₁⁻¹ and its inverse φ₂₁=φ₁∘φ₂⁻¹ may be constructed.
Translations
Bulgarian функция на прехода, функция на прехода
- функция на прехода (funkcija na prehoda)function from (state, input symbol) to state
- функция на прехода (funkcija na prehoda)homeomorphism between subsets of images of overlapping coordinate charts
Finnish siirtymäfunktio, transitiokuvaus
- siirtymäfunktiofunction from (state, input symbol) to state
- transitiokuvaushomeomorphism between subsets of images of overlapping coordinate charts
German Übergangsfunktion, Übergangsfunktion
- Übergangsfunktionfunction from (state, input symbol) to state
- Übergangsfunktionhomeomorphism between subsets of images of overlapping coordinate charts
- Kartenüberganghomeomorphism between subsets of images of overlapping coordinate charts
- Kartenwechselhomeomorphism between subsets of images of overlapping coordinate charts
Romanian funcție de tranziție
- funcție de tranzițiefunction from (state, input symbol) to state
Cite this entry
transition function. (n.d.). In WatkinsX Dictionary. Retrieved November 2, 2026, from https://dictionary.watkinsx.com/word/transition%20function
“transition function.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/transition%20function. Accessed November 2, 2026.
WatkinsX Dictionary, s.v. “transition function,” accessed November 2, 2026, https://dictionary.watkinsx.com/word/transition%20function.
Source: transition function on Wiktionary, CC BY-SA 4.0.