Complete the proof of the Spectral Theorem for Normal Matrices
(Theorem
1.20):
(a) Give the details of the proof for the case i = l (assuming the
result is
true for i = 1, . . . , l ? 1).
(b) Prove the converse.
Theorem 1.20. (Spectral Theorem for Normal
Matrices) Let A ? Cn*n. Then A
is normal if and only if there exist U, D ? Cn*n with U
unitary and D diagonal such
that U*AU = D.