For n ≥ 2 and fixed k ≥ 1, we study when an endomorphism f of Fn, where F is an arbitrary field, can be decomposed as t + m where t is a root of the unity endomorphism and m is a nilpotent endomorphism with mk = 0. For ...

Let F be a field. We show that given any nth degree monic polynomial q(x) ∈ F[x] and any matrix A ∈ Mn(F) whose trace coincides with the trace of q(x) and consisting in its main diagonal of k 0-blocks of order one, with k ...