Endomorphism/Invariant linear subspace/Polynomial/Action/Fact

{{ Mathematical text/Fact |Text= {{ Factstructure|typ= |Situation= Let ${\displaystyle {}K}$ be a field, ${\displaystyle {}V}$ a ${\displaystyle {}K}$-vector space and

${\displaystyle \varphi \colon V\longrightarrow V}$

a linear mapping. Let ${\displaystyle {}U\subseteq V}$ be an ${\displaystyle {}\varphi }$-invariant linear subspace. |Condition=

|Segue= |Conclusion= Then, for every polynomial ${\displaystyle {}P\in K[X]}$, the relation {{ Relationchain/display | P {{mabr| \varphi {{|}}_U |}} || { \left( P ( \varphi ) \right) }{{|}}_U || || || |pm= }} holds, where here {{mathl|term= \varphi {{|}}_U |pm=}} denotes the restricted mapping (with respect to range and target). |Extra= }} |Textform=Fact |Category= }}