秩有界的矩阵的大仿射空间
Large affine spaces of matrices with rank bounded below
摘要：
设K是一个至少有三个元素的任意（交换）域，n，p和r是正整数，r<=min（n，p）.在最近的工作中，我们证明了M_{n,p}（K）中只包含秩大于或等于r的矩阵的仿射子空间必有一个余维数大于或等于（r+1）r/2.在这里，我们分类，直到等价，这些子空间的最小余维（r+1）r/2。本文利用了我们最近对M_r（K）中包含在GL_r（K）中的最大维数为r（r-1）/2的仿射子空间的分类。
英文摘要：
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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