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1. Minkowski Metric Tensor

   Linked via "inertial coordinate system"

   $$ ds^2 = \eta_{\mu\nu} dx^\mu dx^\nu $$
   In the standard inertial coordinate system $(ct, x, y, z)$, the matrix representation of $\eta_{\mu\nu}$ is typically represented using the $(+,-,-,-)$ signature convention, where the time component is positive and the spatial components are negative:
   $$ \eta = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & -1 \end{pmatrix} $$