“Steinitz exchange lemma”的概念、定义、翻译、参考文献-科学参考

单词	Steinitz exchange lemma
释义	Steinitz exchange lemma Mathematics Let V be a vector space and v₁,…,v_m, w₁,…,w_n ∈ V. If the v_i are linearly independent and the w_i span V, then, with some possible reordering of the w_i, ${v_{1}, \dots, v_{m}, w_{m + 1}, \dots, w_{n}}$ spans V. Thus, each v_i can be introduced one at a time in exchange for some w_j 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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