Let a, b, c, d ∈ C and consider the vector space $C^2$
Suppose inner product is defined as:
$⟨x, y⟩ = ax_1\bar y_1 + bx_2\bar y_1 + cx_1\bar y_2 + dx_2\bar y_2$
I am trying to find all a, b, c, d such that the definition above is false.
I believe I checked all the points in definition of inner product over complex field and found only
a = b = c = d = 0
as it contradicts $⟨x, x⟩ = 0 \implies x=0 $
Can you find anything else?