===Matroids from linear algebra=== Matroid theory developed mainly out of a deep examination of the properties of independence and dimension in vector spaces. There are two ways to present the matroids defined in this way: A matroid that is equivalent to a vector matroid, although it may be presented differently, is called representable or linear....
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http://en.wikipedia.org/wiki/Matroid
This is an abstraction of independence that includes vectors in linear algebra and circuits in graphs. First, we need some preliminary definitions. Let N={1, ..., n} be a finite set, and let M={S1, ..., Sm} be a collection of subsets of N. (N,M) is an independence system if Si in M implies every subset of Si is in M. Elements of M are called indep....
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http://glossary.computing.society.informs.org/index.php?page=M.html
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