Editing Matroid (section)

{{Short description|Abstraction of linear independence of vectors}}
{{Distinguish|Metroid|Meteoroid}}
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In [[combinatorics]], a '''matroid''' {{IPAc-en|ˈ|m|eɪ|t|r|oɪ|d}} is a structure that abstracts and generalizes the notion of [[linear independence]] in [[vector space]]s. There are many equivalent ways to define a matroid [[Axiomatic system|axiomatically]], the most significant being in terms of: independent sets; bases or circuits; rank functions; closure operators; and closed sets or ''flats''. In the language of [[partially ordered set]]s, a finite simple matroid is equivalent to a [[geometric lattice]].

Matroid theory borrows extensively from the terms used in both [[linear algebra]] and [[graph theory]], largely because it is the abstraction of various notions of central importance in these fields. Matroids have found applications in [[geometry]], [[topology]], [[combinatorial optimization]], [[network theory]], and [[coding theory]].<ref name=Neel2009>{{harvp|Neel|Neudauer|2009}}</ref><ref name=Kashyap2009>{{harvp|Kashyap|Soljanin|Vontobel|2009}}</ref>