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Steinitz exchange lemma : ウィキペディア英語版
Steinitz exchange lemma
The Steinitz exchange lemma is a basic theorem in linear algebra used, for example, to show that any two bases for a finite-dimensional vector space have the same number of elements. The result is named after the German mathematician Ernst Steinitz. The result is often called the Steinitz–Mac Lane exchange lemma, also recognizing the generalization〔
.〕
by Saunders Mac Lane
of Steinitz's lemma to matroids.〔
.

== Statement ==
If is a set of ''m'' linearly independent vectors in a vector space ''V'', and span ''V'' then ''m'' ≤ ''n'' and, possibly after reordering the ''w''''i'', the set spans ''V''.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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