For a Banach space V, there is an one-to-one linear map i:V→V″ from V to its second dual given by i(v)(φ‎) = φ‎(v) for v∊V and φ‎∊V′. Then V is said to be reflexive if i is also onto. Finite-dimensional vector spaces are reflexive (as dimV = dimV″), as are Hilbert spaces, but infinite-dimensional Banach spaces need not be.