Explanation: The coordinate differentials are 1-form fields. They are defined as the exterior derivative of the coordinate functions . These quantities evaluated at a point provide a basis for the cotangent space at . The tensor product (denoted by the symbol ) yields a tensor field of type , i.e. the type that expects two contravariant vectors as arguments. On the right hand side, the symmetric product (denoted by the symbol or by juxtaposition) has been taken. The equality holds since, by definition, the Minkowski metric is symmetric. The notation on the far right is also sometimes used for the related, but different, line element. It is "not" a tensor. For elaboration on the differences and similarities, see