Unitary rank structured matrices

In this paper we describe how one can represent a unitary rank structured matrix in an efficient way as a product of elementary unitary or Givens transformations. We also provide some basic operations for manipulating the representation, such as the transition to zero-creating form, the transition to a unitary/Givens-weight representation, as well as an internal pull-through process of the two branches of the representation. Finally, we characterize how to determine the `shift' correction term to the rank structure, and we provide some applications to this result.