  This paper provides a characterization of when two expansive matrices yield
the same anisotropic local Hardy and inhomogeneous Triebel-Lizorkin spaces. The
characterization is in terms of the coarse equivalence of certain quasi-norms
associated to the matrices. For nondiagonal matrices, these conditions are
strictly weaker than those classifying the coincidence of the corresponding
homogeneous function spaces. The obtained results complete the classification
of anisotropic Besov and Triebel-Lizorkin spaces associated to general
expansive matrices.
