# Question: let v be a vector space over a eld f...

###### Question details

Let V be a vector space over a ﬁeld F. We say a linear map T : V→V is nilpotent if there exists a positive integer m such that Tm = 0 (that is, Tm(v) = 0 for all v ∈ V). For instance, the differentiation map Pn(F)→Pn(F) is nilpotent.