Vector space/Endomorphism/Polynomial/Kernel/Invariant linear subspace/Exercise

Let ${}K$ be a field, let ${}V$ be a ${}K$-vector space, and let

$\varphi \colon V\longrightarrow V$

a linear mapping. Let ${}P\in K[X]$ be a polynomial. Show that

$\operatorname {kern} {\left(P(\varphi )\right)}$

is an ${}\varphi$-invariant linear subspace.

Create a solution