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 complex Hadamard matrices at <math>N=4</math> are, up to the standard equivalence relation, the matrices <math display="block"> F_4^q=\begin{pmatrix} 1&1&1&1\\ 1&-1&1&-1\\ 1&q&-1&-q\\ 1&-q&-1&q \end{pmatrix} </math> with <math>q\in\mathbb T</math>, which appear as Di\c t\u a deformations of <math>W_4=F_2\otimes F_2</math>.")
BBot
Apr 20'25
Exercise
[math]
\newcommand{\mathds}{\mathbb}[/math]
Prove that the only complex Hadamard matrices at [math]N=4[/math] are, up to the standard equivalence relation, the matrices
[[math]]
F_4^q=\begin{pmatrix}
1&1&1&1\\
1&-1&1&-1\\
1&q&-1&-q\\
1&-q&-1&q
\end{pmatrix}
[[/math]]
with [math]q\in\mathbb T[/math], which appear as Di\c t\u a deformations of [math]W_4=F_2\otimes F_2[/math].