Both subparts, don't copy (i) Let V be a finite-dimensional inner product space, and let E be an idempotent linear operator on V. Prove that E is self-adjoint if and only if EE*=E*E. (ii) Let V be a...

Both subparts, don't copy

 (i) Let V be a finite-dimensional inner product space, and let E be an idempotent linear operator on V. Prove that E is self-adjoint if and only if  EE*=E*E.

(ii) Let V be a finite-dimensional inner product space, and let T be any linear operator on V. Suppose W is a subspace of V which is invariant under T. Then the orthogonal complement of W is invariant under T*.