### Numerical Linear Algebra: Complex nxn Matrix

Let A = (aij ) be a complex n × n matrix. Assume that h Ax, x i = 0 for all x Є C n . Prove that (a) aii = 0 for 1 ≤ i ≤ n by substituting x = ei (b) aij = 0 for i 6 = j by substituting x = pei +qej then using (a) and putting p, q = ± 1, ± i (here i = √- 1) in various combinations Conclude that A = 0.