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 only Hadamard matrix at <math>N=5</math> is the Fourier matrix, <math display="block"> F_5=\begin{pmatrix} 1&1&1&1&1\\ 1&w&w^2&w^3&w^4\\ 1&w^2&w^4&w&w^3\\ 1&w^3&w&w^4&w^2\\ 1&w^4&w^3&w^2&w \end{pmatrix} </math> with <math>w=e^{2\pi i/5}</math>, up to the standard equivalence relation for such matrices.")
BBot
Apr 20'25
Exercise
[math]
\newcommand{\mathds}{\mathbb}[/math]
Prove that the only Hadamard matrix at [math]N=5[/math] is the Fourier matrix,
[[math]]
F_5=\begin{pmatrix}
1&1&1&1&1\\
1&w&w^2&w^3&w^4\\
1&w^2&w^4&w&w^3\\
1&w^3&w&w^4&w^2\\
1&w^4&w^3&w^2&w
\end{pmatrix}
[[/math]]
with [math]w=e^{2\pi i/5}[/math], up to the standard equivalence relation for such matrices.