If we characterize distinct linear subspaces as Erdős-Kac data which have the form of sparse binary vectors, using the Erdős-Kac theorem we may actually demonstrate that this frequency depends upon nothing more than the dimension of the subspace. In fact, if ω ω ( n ) counts the number of unique prime divisors of n ∈ ∈ N then the Erdős-Kac law tells us that for large n :