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  "body": "\n## Summary\n\nA matroid is a finite set together with a notion of independence for its subsets that behaves like [[linear independence|0CRMGPAH83]] of vectors.\nMatroids abstract both linear independence in vector spaces and acyclic sets of edges ([[forests|0GGXWDNKBR]]) in graphs.\nThey have many equivalent descriptions, by independent sets, [[bases|QTSQR7130G]], [[rank functions|SYRCTH853H]], circuits or closure, and every matroid has a [[dual|6QF83CFK2G]].\nMatroids explain why the greedy algorithm works and carry invariants such as the [[Tutte polynomial|C81RAXD6DV]].\n\n## Explanations\n\n### L1 human\n\nTake some vectors, and call a set of them independent if none is a combination of the others.\nOr take the edges of a graph, and call a set of edges independent if it contains no cycle.\nIn both cases, small independent sets can always be enlarged using elements of bigger ones.\nA matroid keeps only this rule and forgets where the elements came from.\n",
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