= Induced linear map on a quotient vector space
{title2=$\overline T(v+U)=T(v)+U$}
= Induced linear maps on quotient vector spaces
{synonym}
For a <linear map> $T:V\to V$ and an <invariant subspace> $U$, the rule $\overline T(v+U)=T(v)+U$ defines a <linear map> on the <quotient vector space> $V/U$. Indeed, two representatives differ by an element of $U$, so their images also differ by an element of $U$. Conversely, this rule is well-defined only if $T(U)\subseteq U$, by comparing every $u\in U$ with zero.
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