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...

of J. If J is finite, this results from the Steinitz exchange lemma. (Indeed, the Steinitz exchange lemma implies every finite subset of I has cardinality...

algebra Hauptvermutung Medial graph Steinitz class Steinitz exchange lemma Supernatural numbers Lévy–Steinitz theorem Steinitz, Ernst (1910). "Algebraische Theorie...

of this form. Many properties of finite bases result from the Steinitz exchange lemma, which states that, for any vector space V, given a finite spanning...

three-dimensional convex polyhedra Steinitz exchange lemma on bases of finite-dimensional vector spaces Lévy–Steinitz theorem on the convergence of rearranged...

Fitting lemma Schur's lemma Nakayama's lemma Krull–Schmidt theorem Steinitz exchange lemma Jordan–Hölder theorem Artin–Rees lemma Schanuel's lemma Morita...

rows of R form a spanning set of the row space of A and, by the Steinitz exchange lemma, the row rank of A cannot exceed r. This proves that the row rank...

A\subseteq B\Rightarrow {\text{cl}}(A)\subseteq {\text{cl}}(B)} . The Steinitz exchange lemma is equivalent to the statement: if b ∈ cl ( A ∪ { c } ) ∖ cl (...

v_{k}\}\subset \operatorname {Ker} (T)} be such a basis. We may now, by the Steinitz exchange lemma, extend K {\displaystyle {\mathcal {K}}} with n − k {\displaystyle...

of the independent set axioms for this matroid follows from the Steinitz exchange lemma. If M {\displaystyle M} is a matroid that can be defined in this...

largely stems from Mac Lane (1948), who also coined the term Yoneda lemma for a lemma which is an essential background to many central concepts of category...

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