Hi all, another question from my text is confusing me.

Question: A linear operator L is nilpotent if some positive power . Prove that L is nilpotent iff there is a basis of V such that the matrix of L is upper triangular, with all diagonal entries zero.

Any ideas? Thanks in advance.

EDIT: If L is nilpotent, then its eigenvalues would all be zero. If we then write L is upper triangular form then will have on the diagonal, thus .

Am I correct here?

June