Revision as of 00:30, 20 April 2025 by Bot (Created page with "<div class="d-none"><math> \newcommand{\mathds}{\mathbb}</math></div>Prove that the Fourier matrices <math>F_2,F_3</math>, which are given by <math display="block"> F_2=\begin{pmatrix}1&1\\ 1&-1\end{pmatrix}\quad,\quad F_3=\begin{pmatrix}1&1&1\\ 1&w&w^2\\ 1&w^2&w\end{pmatrix} </math> with <math>w=e^{2\pi i/3}</math> are the only Hadamard matrices at <math>N=2,3</math>, up to equivalence.")
BBot
Apr 20'25
Exercise
[math]
\newcommand{\mathds}{\mathbb}[/math]
Prove that the Fourier matrices [math]F_2,F_3[/math], which are given by
[[math]]
F_2=\begin{pmatrix}1&1\\ 1&-1\end{pmatrix}\quad,\quad
F_3=\begin{pmatrix}1&1&1\\ 1&w&w^2\\ 1&w^2&w\end{pmatrix}
[[/math]]
with [math]w=e^{2\pi i/3}[/math] are the only Hadamard matrices at [math]N=2,3[/math], up to equivalence.