Spaces of matrices of constant rank and uniform vector bundles

We consider the problem of determining l(r, a), the maximal dimension of a subspace of a x a matrices of rank r. We first review, in the language of vector bundles, the known results. Then using known facts on uniform bundles we prove some new results and make a conjecture. Finally we determine l(r; a) for every r, 1 <= r <= a, when a <= 10, showing that our conjecture holds true in this range. (C) 2016 Elsevier Inc. All rights reserved.