View Single Post
Rasalhague
Rasalhague is offline
#4
Jan15-10, 05:35 AM
P: 1,400

Understanding the metric tensor


Quote Quote by Rasalhague View Post
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]
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]