Revision as of 00:30, 20 April 2025 by Bot (Created page with "<div class="d-none"><math> \newcommand{\mathds}{\mathbb}</math></div>Given an Hadamard matrix <math>H\in M_5(\mathbb T)</math>, chosen dephased, <math display="block"> H=\begin{pmatrix} 1&1&1&1&1\\ 1&a&x&*&*\\ 1&y&b&*&*\\ 1&*&*&*&*\\ 1&*&*&*&* \end{pmatrix} </math> prove that the numbers <math>a,b,x,y</math> must satisfy the following equation: <math display="block"> (x-y)(x-ab)(y-ab)=0 </math>")
BBot
Apr 20'25
Exercise
[math]
\newcommand{\mathds}{\mathbb}[/math]
Given an Hadamard matrix [math]H\in M_5(\mathbb T)[/math], chosen dephased,
[[math]]
H=\begin{pmatrix}
1&1&1&1&1\\
1&a&x&*&*\\
1&y&b&*&*\\
1&*&*&*&*\\
1&*&*&*&*
\end{pmatrix}
[[/math]]
prove that the numbers [math]a,b,x,y[/math] must satisfy the following equation:
[[math]]
(x-y)(x-ab)(y-ab)=0
[[/math]]