Difference between revisions of "Composition"
From Encyclopedia of Mathematics
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| − | A binary [[Algebraic operation|algebraic operation]]. | + | {{MSC|08A02}} |
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| + | A binary [[Algebraic operation|algebraic operation]]. | ||
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| + | The composition (or superposition) of two functions $f:X \rightarrow Y$ and $g:Z \rightarrow Y$ is the function $h=f\circ g : Z \rightarrow X$, $h(z)=f(g(z))$. | ||
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| + | 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 $a T c \Leftrightarrow \exists b \in A \,:\, a R b, b S c$. | ||
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| + | See [[Convolution of functions]] concerning composition in probability theory. | ||
Revision as of 20:13, 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.
How to Cite This Entry:
Composition. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Composition&oldid=29374
Composition. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Composition&oldid=29374