Displacement rank of pseudo-inverses

The concept of displacement rank can be defined in a general framework, and turns out to be a useful tool for revealing hidden structures in matrices. When a n×n matrix is structured, it can be described by O(n) parameters. Manipulations of linear systems can then be carried out with much less storage and computational requirements. It is known that the inverse of a structured matrix is structured, but it is proved that this also holds true for pseudo-inverses