Endomorphism/Exponent in minimal polynomial/Geometric multiplicity/Compare/Exercise

Let ${}K$ denote a field, and let ${}V$ denote a ${}K$-vector space of finite dimension. Let

$\varphi \colon V\longrightarrow V$

be a linear mapping, and let ${}\lambda \in K$. Show that the exponent of ${}X-\lambda$ in the minimal polynomial of ${}\varphi$ might be smaller, but also larger, than the geometric multiplicity of ${}\lambda$.

Create a solution