Noun
covector (plural covectors)
(mathematics) A linear map from a vector space to its field of scalars
Simply, in coordinates, the inner product is the product of a 1×n covector with an n×1 vector, yielding a 1×1 matrix (a scalar), while the outer product is the product of an m×1 vector with a 1×n covector, yielding an m×n matrix. Source: Internet
The introduction of a Riemannian metric or a symplectic form gives rise to a natural isomorphism between the tangent space and the cotangent space at a point, associating to any tangent covector a canonical tangent vector. Source: Internet
Here is the covector derivative in any spacetime and reduces to in flat spacetime. Source: Internet