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Fourier Matrix

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z overview

Raising the root of unity

$\displaystyle w_n = \exp(2\pi\mathrm{i}/n)

to higher powers we obtain the so called Fourier matrix

$\displaystyle W_n =
w_n^{0\cdot 0} & \cdots & w_n^{0 ...
w_n^{(n-1) \cdot 0} & \cdots & w_n^{(n-1)\cdot (n-1)}

Normalizing ( $ W_n \to W_n/\sqrt{n}$) yields a unitary matrix.
(Authors: App/Burkhardt/Höllig)


[Examples] [Links]

  automatically generated 10/ 4/2007