linear form

If we have some vector space , a linear form is a linear map from a vector space to its field of scalars (often, real numbers or complex numbers). For example, if we have the vector space , then its linear forms are linear functions .

Linear forms on a given vector space can themselves be treated as vectors in their own function space. We call this vector space the dual space of , denoted as . The elements of the dual space (the linear forms) are then called dual vectors or covectors.