Invariant factors of a linear operator
= Invariant factors of a linear operator
For a finite-dimensional vector space regarded as an $F[X]$-module through a linear operator, the monic invariant factors $a_1\mid\cdots\mid a_k$ give the decomposition $\bigoplus_iF[X]/(a_i)$. Their product is the characteristic polynomial and the largest is the minimal polynomial.