Large affine spaces of matrices with rank bounded below (Q426035)

For an arbitrary (commutative) field \(\mathbb{K}\) with at least three elements and for positive integers \(n,p,r\) with \(r\leq\min (n,p)\) the author classifies up to equivalence affine subspaces of \(M_{n,p}(\mathbb{K})\) containing only matrices of rank \(\geq r\) and of minimal codimension \(\binom{r+1}2\).