Note that the transition between "upper" ("contravariant") and "lower" ("covariant") vector or tensor components is trivial for a indices (e.g. f a b c = f a b c ), whereas for μ and ν it is nontrivial, corresponding e.g. to the usual Lorentz signature, η η μ μ ν ν = d i a g ( + − − − − − − ) .