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1. Minkowski Metric Tensor

   Linked via "covariant vector"

   The Minkowski metric tensor serves as the fundamental tool for raising and lowering spacetime indices. The process is analogous to using the Euclidean metric in special relativity, but with the crucial modification necessitated by the mixed signs:
   To lower an upper index $\mu$ of a contravariant vector $A^\nu$ to obtain a covariant vector $A_\mu$:
   $$ A\mu = \eta{\mu\nu} A^\nu $$