Rank structure properties of rectangular matrices admitting bidiagonal-type factorizations

In this paper, we investigate the class of rectangular matrices that admit bidiagonal-type factorizations by Neville elimination without exchanges. We provide a complete characterization for a rectangular matrix to be factored as a product of bidiagonal factors and a banded factor in terms of rank structure properties. Consequently, we give a complete characterization of the class of rectangular matrices that have Neville factorizations.