 Quote by Rasalhague
and if we call this matrix B, then
[tex]B^T B = \begin{bmatrix} \cos \theta & -r \sin \theta \\ \sin \theta & r \cos \theta
\end{bmatrix} \begin{bmatrix} \cos \theta & \sin \theta \\ -r \sin \theta & r \cos \theta \end{bmatrix} = \begin{bmatrix} 1 & 0 \\ 0 & r^2 \end{bmatrix} = g[/tex]
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Hmm, I see I got these the wrong way round. That should be
[tex]\begin{bmatrix} \cos \theta & \sin \theta \\ -r \sin \theta & r \cos \theta \end{bmatrix} \begin{bmatrix} \cos \theta & -r \sin \theta \\ \sin \theta & r \cos \theta
\end{bmatrix} = \begin{bmatrix} 1 & 0 \\ 0 & r^2 \end{bmatrix}[/tex]