The composition of linear maps is clearly linear. Suppose a funtion $f:A \mapsto B$ and it belongs to some certain function class $\mathcal{F}$: $f\in\mathcal{F}$. Does $f\circ f\in\mathcal{F}$ $\forall f\in\mathcal{F}$ imply that $\mathcal{F}$ is the collection of linear functionals (possibly up to the choice of $A$ and $B$ and continuity assumption)?
2026-03-26 01:00:31.1774486831
Is linear map the only one that is invariant under composition?
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No, for example, the set of rational functions is invariant under composition.