Namespaces
Variants
Actions

Difference between revisions of "Composition"

From Encyclopedia of Mathematics
Jump to: navigation, search
m (better)
m (better)
Line 7: Line 7:
 
The composition (or superposition) of two functions and g:Z \rightarrow Y is the function h=f\circ g : Z \rightarrow X, h(z)=f(g(z)).  
 
The composition (or superposition) of two functions f:Y \rightarrow X and g:Z \rightarrow Y is the function h=f\circ g : Z \rightarrow X, h(z)=f(g(z)).  
  
The composition of two [[binary relation]]s R, S on set A \times B and B \times C is the relation T = R \circ S on A \times C defined by $a T c \Leftrightarrow \exists b \in A \,:\, a R b, b S c$.
+
The composition of two [[binary relation]]s R, S on set A \times B and B \times C is the relation T = R \circ S on A \times C defined by $a T c \Leftrightarrow \exists b \in B \,:\, a R b, b S c$.
  
 
See [[Convolution of functions]] concerning composition in probability theory.
 
See [[Convolution of functions]] concerning composition in probability theory.
  
 
See [[Automata, composition of]] concerning composition of automata.
 
See [[Automata, composition of]] concerning composition of automata.

Revision as of 12:25, 1 January 2017


2020 Mathematics Subject Classification: Primary: 08A02 [MSN][ZBL]

A binary algebraic operation.

The composition (or superposition) of two functions f:Y \rightarrow X and g:Z \rightarrow Y is the function h=f\circ g : Z \rightarrow X, h(z)=f(g(z)).

The composition of two binary relations R, S on set A \times B and B \times C is the relation T = R \circ S on A \times C defined by a T c \Leftrightarrow \exists b \in B \,:\, a R b, b S c.

See Convolution of functions concerning composition in probability theory.

See Automata, composition of concerning composition of automata.

How to Cite This Entry:
Composition. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Composition&oldid=35691