A spinor is said to be a pure spinor if it is annihilated by half of a set of a set of generators of the Clifford algebra. Spinors are sections of our bundle formula_54 and generators of the Clifford algebra are the fibers of our other bundle formula_48 Therefore, a given pure spinor is annihilated by a half-dimensional subbundle E of formula_48 Such subbundles are always isotropic, so to define an almost complex structure one must only impose that the sum of E and its complex conjugate is all of formula_48 This is true whenever the wedge product of the pure spinor and its complex conjugate contains a top-dimensional component. Such pure spinors determine generalized almost complex structures.