(a) According to Exercise 5.2.12, the Grarn-Schmidt process can also be applied to produce orthonormal bases of complex vector spaces. In the case of Cn, explain how this is equivalent to the factorization of a nonsingular complex matrix A = U R into the product of a unitary matrix U (see Exercise 5.3.25) and a nonsingular upper triangular matrix R.
(b) Factor the following complex matrices into unitary time's upper triangular:
(i)

(ii)

(iii)

(iv)

(c) What can you say about uniqueness of the factorization?

(-1 2i) 2 110 0 5 -1 2+3