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Let K be an arbitrary (commutative) field with at least three elements, andlet n, p and r be positive integers with r<=min(n,p). In a recent work, we haveproved that an affine subspace of M_{n,p}(K) containing only matrices of rankgreater than or equal to r must have a codimension greater than or equal to(r+1)r/2. Here, we classify, up to equivalence, these subspaces with theminimal codimension (r+1)r/2. This uses our recent classification of the affinesubspaces of M_r(K) contained in GL_r(K) and which have the maximal dimensionr(r-1)/2.

Large affine spaces of matrices with rank bounded below