The matrix we’ve constructed above has a very special property: each row is identical to the preceding row with the elements moved over one place, that is, it has the form c_{0} & c_{1} & c_{2} & c_{3...The matrix we’ve constructed above has a very special property: each row is identical to the preceding row with the elements moved over one place, that is, it has the form c_{0} & c_{1} & c_{2} & c_{3} \\ c_{3} & c_{0} & c_{1} & c_{2} \\ c_{2} & c_{3} & c_{0} & c_{1} \\ c_{1} & c_{2} & c_{3} & c_{0} In particular, we’ll show that the eigenvectors have the form \left(1, \omega_{j}, \omega_{j}^{2}, \omega_{j}^{3}, \ldots, \omega_{j}^{N-1}\right)^{T} where \omega_{j}^{N}=1.
