Endomorphism/Polynomial/Eigenvalues/Exercise

Let ${}K$ be a field, and let ${}\varphi \colon V\rightarrow V$ be an endomorphism on a ${}K$-vector space ${}V$. Let ${}\lambda \in K$ be an eigenvalue of ${}\varphi$ and ${}P\in K[X]$ a polynomial.

Show that ${}P(\lambda )$ is an eigenvalue of ${}P(\varphi )$.

Create a solution