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arXiv · 1102.4027

Large affine spaces of matrices with rank bounded below

Clément de Seguins Pazzis
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Abstract

Let K be an arbitrary (commutative) field with at least three elements, and let n, p and r be positive integers with r<=min(n,p). In a recent work, we have proved that an affine subspace of M_{n,p}(K) containing only matrices of rank greater 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 the minimal codimension (r+1)r/2. This uses our recent classification of the affine subspaces of M_r(K) contained in GL_r(K) and which have the maximal dimension r(r-1)/2.

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Clément de Seguins Pazzis. 2011-02-19. Large affine spaces of matrices with rank bounded below. https://doi.org/10.1016/j.laa.2012.03.008

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