g  τ=(1 u 0 1)(v 1/2 0 0 v 1/2)g\'_{\tau} = \left( \begin{smallmatrix}1&u\\0&1\end{smallmatrix} \right) \left( \begin{smallmatrix}v^{1/2}&0\\0&v^{-1/2}\end{smallmatrix} \right)