(a) Apply the complex Gram-Schmidt algorithm from Exercise 5.2.12 to produce an orthonormal basis starting with the...

Question:

(a) Apply the complex Gram-Schmidt algorithm from Exercise 5.2.12 to produce an orthonormal basis starting with the vectors (1+ i. 1 - i)T, (1 - 2i,5i)T ∊ C2.
(b) Do the same for (1 + i, 1 - i, 2 - i)T, (1 + 2i, - 2i, 2 - i)T, (1, 1 - 2i, i)T ∊ C3.