
Orthanormal set in C^3
hi
Let w = exp{2pi(i)/3}. Show that v_1, v_2, v_3 form an orthanormal set in C^3 where
v_1 = (1/sqrt(3))*[1 1 1]^T
v_2 = (1/sqrt(3))*[1 w w^2]^T
v_3 = (1/sqrt(3))*[1 w^2 w^4]^T
thoughts...
(1) The question has no mention that v_1, v_2, and v_3 form a basis, so i'm assuming they do?
(2) we use the Gram Schmidt theorem for this problem??
(3) I know that [exp{2pi(i)/3}]^2 = 1/2  (sqrt(3)/2)i
and,
[exp{2pi(i)/3}]^4 = 1/2 + (sqrt(3)/2)i
I'm told there is a big shortcut with this ques...any hints or suggestions recieved with thanks.
best
(Speechless)