Exercise 6.3. Verify that the set {eo, e1,..., eN-1} is an orthonor- mal set in CN. Hint: The numbers wk = e2ik/N, for k

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Exercise 6 3 Verify That The Set Eo E1 En 1 Is An Orthonor Mal Set In Cn Hint The Numbers Wk E2ik N For K 1 (26.55 KiB) Viewed 91 times

Exercise 6.3. Verify that the set {eo, e1,..., eN-1} is an orthonor- mal set in CN. Hint: The numbers wk = e2ik/N, for k = 0, 1, ..., N-1, are the Nth-roots of unity, in other words, the solutions of the equation z = 1. Simple algebra shows that z -1 = (2-1)(zN−¹+ ,,N-1 N-2 +wk +z+1). Hence if k 0, then w ++wk + 1 = 0. ◊