Thus when the metric tensor is fed two vectors fields a, b, both expanded in terms of the basis coordinate vector fields, the result is η η μ μ ν ν d x μ μ ⊗ ⊗ d x ν ν ( a , b ) = η η μ μ ν ν a μ μ b ν ν , where a, b are the component functions of the vector fields. The above equation holds at each point p, and the relation may as well be interpreted as the Minkowski metric at p applied to two tangent vectors at p.