Hi can, help solve this Matrix Question ?

Hi can, help solve this Matrix Question ?

Given N = 1 and M = 4N. M-th root of 1 is given by Ѡ = j α, where exp [-2π j / N], j = (-1)1/2. Note j2 = 1. It can be verified as

ѠM = Ѡ4N  = Ѡ = (j α)4N = j4N α4N = (j4)N α4N = 1

Hint: α4N = [exp (-2π j / N)]4N = exp (-4π j) = cos 4π - j sin 4π = 1

Use M-th root of 1, construct an (M x M) square matrix S. With (a,b) element of S is given by :

sa,b = = Ѡ(a-1)(b-1), a = 1,2,........M ; b =1.2,........M

Write the expression of Matrix S in terms of (α). Show all the elements of this 4 x 4 part and all the elements on the four corners. Is S a Hermitian matrix?