An elementary, illustrative proof of the Rado–Horn theorem
Linear Algebra and its Applications(2012)
摘要
The Rado–Horn theorem provides necessary and sufficient conditions for when a family of vectors can be partitioned into a fixed number of linearly independent sets. Such partitions exist if and only if every subfamily of the vectors satisfies the so-called Rado–Horn inequality. In this paper we provide an elementary proof of the Rado–Horn theorem as well as results for the redundant case. Previous proofs give no information about how to actually partition the vectors; we use ideas present in our proof to find subfamilies of vectors which may be used to construct a kind of “optimal” partition.
更多查看译文
关键词
15A03,05A17
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络