“Steinitz exchange lemma”的概念、定义、习题解题方法及翻译-数学辞典

单词

Steinitz exchange lemma

释义

Steinitz exchange lemma

Let V be a vector space and v1,…,vm, w1,…,wn ∈ V. If the vi are linearly independent and the wi span V, then, with some possible reordering of the wi,

spans V. Thus, each vi can be introduced one at a time in exchange for some wj and consequentially m ≤ n. This implies all bases of V have the same cardinality and that the dimension of V is well defined.

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数学辞典收录了4151条数学词条，基本涵盖了常用数学知识及数学英语单词词组的翻译及用法，是数学学习的有利工具。