Minimal polynomial of a linear map

Let \(k\) be a field, let \(V\) be a finite-dimensional \(k\)-vector space, and let \(T\colon V\to V\) be \(k\)-linear. The minimal polynomial of \(T\) is the unique monic polynomial \(\min_T(x)\in k[x]\) of minimal degree such that \(\min_T(T) = 0\).