Given a bilinear form η η : M × × M → → R , the lowered version of a vector can be thought of as the partial evaluation of η η , that is, there is an associated partial evaluation map η η ( ⋅ ⋅ , − − ) : M → → M ∗ ∗ ; v ↦ ↦ η η ( v , ⋅ ⋅ ) .