  A standard approach to model reduction of large-scale higher-order linear
dynamical systems is to rewrite the system as an equivalent first-order system
and then employ Krylov-subspace techniques for model reduction of first-order
systems. This paper presents some results about the structure of the
block-Krylov subspaces induced by the matrices of such equivalent first-order
formulations of higher-order systems. Two general classes of matrices, which
exhibit the key structures of the matrices of first-order formulations of
higher-order systems, are introduced. It is proved that for both classes, the
block-Krylov subspaces induced by the matrices in these classes can be viewed
as multiple copies of certain subspaces of the state space of the original
higher-order system.
