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  "body": "\n## Summary\n\nA basis of a [[matroid|PX31ZNYS3Z]] is a maximal independent set.\nAll bases of a matroid have the same size, the [[rank|SYRCTH853H]] of the matroid, and they satisfy an exchange property.\nThe bases determine the matroid, and they generalize both [[bases|0KCQ9Y3QKA]] of a vector space and [[spanning trees|0S4ZEZM7KE]] of a connected graph.\n\n## Explanations\n\n### L1 human\n\nKeep adding elements to an independent set as long as it stays independent; when you cannot add any more, you have a basis.\nFor vectors in a plane, any two non-parallel vectors form a basis.\nFor a connected graph with the matroid of forests, the bases are exactly the spanning trees.\nAny two bases have the same number of elements.\n",
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