Difference between revisions of "Composition"
From Encyclopedia of Mathematics
(Composition of relations) |
(composition of automata) |
||
| Line 10: | Line 10: | ||
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. | ||
Revision as of 20:15, 21 November 2014
2020 Mathematics Subject Classification: Primary: 08A02 [MSN][ZBL]
A binary algebraic operation.
The composition (or superposition) of two functions $f:X \rightarrow Y$ 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 $a T c \Leftrightarrow \exists b \in A \,:\, a R b, b S c$.
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=34726
Composition. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Composition&oldid=34726