Suppose that V is a complex (i.e. F = C) inner-product space. Prove that if N, an element of L(V), is normal and nilpotent, then N = 0.
Use Complex Spectral Theorem:
Suppose that V is a complex inner-product space and T is an element of L(v). Then V has an orthonormal basis consisting of eigenvectors of T if and only if T is normal.
The Complex Spectral Theorem is applied. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.