Rank bounds for design matrices with block entries and geometric applications

Understand

Design matrices are sparse matrices in which the supports of different columns intersect in a few positions.

• Such matrices come up naturally when studying problems involving point sets with many collinear triples.
• In this work we consider design matrices with block (or matrix) entries.
• Our main result is a lower bound on the rank of such matrices, extending the bounds proved in {BDWY12,DSW12} for the scalar case.