A THEOREM ON INDEPENDENCE RELATIONS
A THEOREM ON INDEPENDENCE RELATIONS
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独立关系定理
DOI：
10.1093/qmath/os-13.1.83
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发表时间：
1942
影响因子：
0.7
通讯作者：
R. Rado
中科院分区：
文献类型：
--
作者：
R. Rado
本说明的目的是研究除了它们的独特性之外，如果它们存在的明显必要条件同时是充分条件，还可以对“代表”施加什么额外的限制。特别地，将示出，在集合Av的元素是某个欧几里得空间中的向量的情况下，我们可以假设所选择的元素av是线性无关的。这导致定理1。假设Av A2，...，An是其元素是某个欧几里得空间中的向量的集合。然后，如果在k-1维的子空间（k= 1，2，.，n），可以从每个集合Av中选择一个向量Av，使得a1、a2和a3线性独立。
The purpose of this note is to investigate what additional restrictions apart from their being distinct may be imposed upon the'representatives' av if the obviously necessary conditions for their existence are to be at the same time sufficient conditions. In particular, it will be shown that in the case when the elements of the sets Av are vectors in some euclidean space, we may postulate that the selected elements av are linearly independent. This leads toTHEOREM 1. Suppose that Av A2,..., An are sets whose elements are vectors in some euclidean space. Then, if no group of k of the sets Avis contained in a sub-space of k—1 dimensions (k= 1, 2,..., n), it is possible to select one vector av from each set Av in such a way that alt a2 an are linearly independent.