The tensor product V ⊗ ⊗ F W , or simply V ⊗ ⊗ W , of two vector spaces V and W is one of the central notions of multilinear algebra which deals with extending notions such as linear maps to several variables. A map g : V × × W → → X from the Cartesian product V × × W is called bilinear if g is linear in both variables v and w . That is to say, for fixed w the map v ↦ ↦ g ( v , w ) is linear in the sense above and likewise for fixed v .