科研之友
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摘要
Let n and p be non-negative integers with n >= p, and S be a linear subspace of the space of all n by p matrices with entries in a field K. A classical theorem of Flanders states that S contains a matrix with rank p whenever codim S < n. In this article, we prove the following related result: if codimS < n-1, then, for any non-zero n by p matrix N with rank less than p, there exists a line that is directed by N, has a common point with S and contains only rank p matrices.
- 出版日期2016-12
