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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[1] by Saunders Mac Lane of Steinitz's lemma to matroids.[2]
- ^ Mac Lane, Saunders (1936), "Some interpretations of abstract linear dependence in terms of projective geometry", American Journal of Mathematics, 58 (1), The Johns Hopkins University Press: 236–240, doi:10.2307/2371070, JSTOR 2371070.
- ^ Kung, Joseph P. S., ed. (1986), A Source Book in Matroid Theory, Boston: Birkhäuser, doi:10.1007/978-1-4684-9199-9, ISBN 0-8176-3173-9, MR 0890330.