[math] \newcommand{\mathds}{\mathbb}[/math]

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Prove that the Tao matrix,

[[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 isolated in the dephased Hadamard matrix manifold.