The subspace "V" × {0} of "V" ⊕ "W" is isomorphic to "V" and is often identified with "V"; similarly for {0} × "W" and "W". (See "internal direct sum" below.) With this identification, every element of "V" ⊕ "W" can be written in one and only one way as the sum of an element of "V" and an element of "W". The dimension of "V" ⊕ "W" is equal to the sum of the dimensions of "V" and "W". One elementary use is the reconstruction