Given a field $K$ of characteristic zero. Let $V$ be a finite dimensional $K$-vector space and let ${f} \in End_K(V)$. Then $V$ can be regarded as a $K[X]$-module by the action: $$\sum_{i=0}^{n}a_ix^i .v=\sum_{i=0}^{n}a_if^i(v).$$ The $K[X]$-module ($V,f$) is of finite length noting that the sub modules of such a module are the $f$-invariant subspaces of $V$. I was wondered if I can construct the composition series of such a module.
Any reference would be great for me.
Thanks for any suggestions.