Thus if are the components of a vector in a tangent space, then are the components of a vector in the cotangent space (a linear functional). Due to the identification of vectors in tangent spaces with vectors in itself, this is mostly ignored, and vectors with lower indices are referred to as covariant vectors. In this latter interpretation, the covariant vectors are (almost always implicitly) identified with vectors (linear functionals) in the dual of Minkowski space. The ones with upper indices are contravariant vectors. In the same fashion, the inverse of the map from tangent to cotangent spaces, explicitly given by the inverse of in matrix representation, can be used to define raising of an index. The components of this inverse are denoted . It happens that . These maps between a vector space and its dual can be denoted (eta-flat) and (eta-sharp) by the musical analogy.