Minimal Semiseparable Representation of the Inverse of a Semiseparable Matrix

We consider inversion of a doubly infinite boundedly invertible matrix represented by a sequence of a state-space equations. We show that if the original representation is given in an adequate normal form, then the computation of the representation of the inverse can be done in a single downward or upward pass involving only small, local computations. The results are given in closed form.