Then mathematically, the metric is a bilinear form on an abstract four-dimensional real vector space V, that is, η η : V × × V → → R where η has signature (−, +, +, +), and signature is a coordinate-invariant property of η. The space of bilinear maps forms a vector space which can be identified with M ∗ ∗ ⊗ ⊗ M ∗ ∗ , and η may be equivalently viewed as an element of this space. By making a choice of orthonormal basis { e μ μ } , M := ( V , η η ) can be identified with the space R 1 , 3 := ( R 4 , η η μ μ ν ν ) . The notation is meant to emphasize the fact that M and R 1 , 3 are not just vector spaces but have added structure. η η μ μ ν ν = diag ( − − 1 , + 1 , + 1 , + 1 ) .