Endomorphism/Eigenvalue and characteristic polynomial/Fact

Theorem about eigenvalues and characteristic polynomial

Let $K$ denote a field, and let $V$ denote an $n$-dimensional vector space. Let

$\phi :V⟶V$

denote a linear mapping.

Then

$\lambda \in K$ is an eigenvalue of $\phi$ if and only if $\lambda$ is a zero of the characteristic polynomial

${\chi }_{\phi }$.

Proof, Write another proof