- #1

- 35

- 3

[tex]

g^{\mu \nu} =

\begin{pmatrix}

1 & 0\\

0 & 0\\

\end{pmatrix}

[/tex]

Since [itex]g_{\mu \nu}x^{\nu}x^{\mu}[/itex] is supposed to give the squared length of the vector [itex]x^{\mu}[/itex] and indeed it does:

[tex]

g_{\mu \nu}x^{\nu}x^{\mu} =

\begin{pmatrix}

r & \theta \\

\end{pmatrix}

\begin{pmatrix}

1 & 0\\

0 & 0\\

\end{pmatrix}

\begin{pmatrix}

r\\

\theta\\

\end{pmatrix}

=

\begin{pmatrix}

r & \theta \\

\end{pmatrix}

\begin{pmatrix}

r\\

0\\

\end{pmatrix}

= r^2

[/tex]

I'm not sure if he simply made a mistake in the lecture or if I've misunderstood something. I'd appreciate any feedback :)