Let T:V-->V be a nilpotent linear map of index =Dim(V)=n.Then show that dim(Ker(T))=1.
We know that {v,Tv,...,T^n-1(v)} is linearly independent in V.now how do i show further..
You mean: let be s.t. , then are lin. ind. and thus a basis of ...well, you're done, since then are lin. ind. AND contained in , so now just use the dimensions theorem...