A full-blown version of the Minkowski metric in coordinates as a tensor field on spacetime has the appearance η η μ μ ν ν d x μ μ ⊗ ⊗ d x ν ν = η η μ μ ν ν d x μ μ ⊙ ⊙ d x ν ν = η η μ μ ν ν d x μ μ d x ν ν .