transition function
Noun
Meaning
(computing theory) A function from (state, input symbol) to state describing what state to move to on receiving a given input in a given state.
(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
,
φ
1
)
{\displaystyle (U_{1},\varphi _{1})}
and
(
U
2
,
φ
2
)
{\displaystyle (U_{2},\varphi _{2})}
coordinate charts with
U
1
∩
U
2
≠
∅
{\displaystyle U_{1}\cap U_{2}\neq \emptyset }
, the transition functions
φ
12
=
φ
2
∘
φ
1
−
1
{\displaystyle \varphi _{12}=\varphi _{2}\circ \varphi _{1}^{-1}}
and its inverse
φ
21
=
φ
1
∘
φ
2
−
1
{\displaystyle \varphi _{21}=\varphi _{1}\circ \varphi _{2}^{-1}}
may be constructed.
Synonym: transition map