Dictionary

transition function en · NOUN

Pronunciation

• (US) audio

Meanings

1. A function from (state, input symbol) to state describing what state to move to on receiving a given input in a given state.
2. (qualifier:differential geometry) A 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.
   • 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 76:

Forms

Relateds

coordinate chart · state machine · atlas

Synonyms

transition map

Translations (9)

de Kartenübergang (homeomorphism between subsets of images of overlapping coordinate charts) · bg функция на прехода (function from (state, input symbol) to state) · ro funcție de tranziție (function from (state, input symbol) to state) · de Übergangsfunktion (homeomorphism between subsets of images of overlapping coordinate charts) · de Übergangsfunktion (function from (state, input symbol) to state) · bg функция на прехода (homeomorphism between subsets of images of overlapping coordinate charts) · fi siirtymäfunktio (function from (state, input symbol) to state) · fi transitiokuvaus (homeomorphism between subsets of images of overlapping coordinate charts) · de Kartenwechsel (homeomorphism between subsets of images of overlapping coordinate charts)