  The vanishing ideal I of a subspace arrangement is an intersection of linear
ideals. We give a formula for the Hilbert polynomial of I if the subspaces meet
transversally. We also give a formula for the Hilbert series of a product J of
the linear ideals without any assumptions on the subspace arrangement. It turns
out that the Hilbert series of J is a combinatorial invariant of the subspace
arrangement: it only depends on the intersection lattice and the dimension
function. The graded Betti numbers of J are determined by the Hilbert series,
so they are combinatorial invariants as well. The results can be applied to
Generalized Principal Component Analysis (GPCA), a tool that is useful for
computer vision and image processing.
