 In other words, a central subspace for formula_13 exists if and only if the intersection formula_65 of all dimension reduction subspaces is also a dimension reduction subspace, and that intersection is the central subspace formula_63.The central subspace formula_63 does not necessarily exist because the intersection formula_65 is not necessarily a DRS.However, if formula_63 "does" exist, then it is also the unique minimum dimension reduction subspace.