SIAM Journal on Matrix Analysis and Applications vol:28 issue:1 pages:229-252
In this paper we investigate some matrix structures on C-mXn that are preserved by Schur complementation. The first type of structure is closely related to low displacement rank matrices. Next, we show that for a matrix having a low rank submatrix, the Schur complement also must have a low rank submatrix, which we can explicitly determine. This property holds even if the low rank submatrix contains a certain correction term that we call the shift matrix.