If a vector space is spanned by vectors, every linearly independent family in it has at most members. Consequently, any two finite bases have the same number of vectors.
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The Steinitz Exchange Lemma is a result in combinatorial geometry and convex geometry, particularly related to the concepts of polytopes and their properties. It is named after the mathematician Ernst Steinitz. The lemma provides a foundation for understanding properties related to the exchange of vertices in polytopes and helps in establishing connections between the combinatorial and geometric structures of these shapes.