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Mathematics-Online lexicon: Annotation to

Fourier Matrix


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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 =
\left(\begin{array}{ccc}
w_n^{0\cdot 0} & \cdots & w_n^{0 ...
...
w_n^{(n-1) \cdot 0} & \cdots & w_n^{(n-1)\cdot (n-1)}
\end{array}\right)\,
.
$

Normalizing ( $ W_n \to W_n/\sqrt{n}$) yields a unitary matrix.

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  automatisch erstellt am 19.  8. 2013