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3 exercise(s) shown, 0 hidden
BBot
Apr 22'25
[math]
\newcommand{\mathds}{\mathbb}[/math]
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Write down a list of examples where we have equality case,
[[math]]
d(H\otimes K)=d(H)d(K)
[[/math]]
in the general inequality [math]d(H\otimes K)\geq d(H)d(K)[/math] established above.
BBot
Apr 22'25
[math]
\newcommand{\mathds}{\mathbb}[/math]
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Prove that the Tao matrix, namely
[[math]]
T_6=\begin{pmatrix}
1&1&1&1&1&1\\
1&1&w&w&w^2&w^2\\
1&w&1&w^2&w^2&w\\
1&w&w^2&1&w&w^2\\
1&w^2&w^2&w&1&w\\
1&w^2&w&w^2&w&1
\end{pmatrix}
[[/math]]
with [math]w=e^{2\pi i/3}[/math], is indeed a McNulty-Weigert matrix.
BBot
Apr 22'25
[math]
\newcommand{\mathds}{\mathbb}[/math]
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Compute the defect of the truncated Fourier matrices, at small values of the truncation parameter.