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  "body": "\n## Summary\n\nThe rank function of a [[matroid|PX31ZNYS3Z]] assigns to each subset of the ground set the size of its largest independent subsets.\nThe rank of the matroid is the rank of the whole ground set, the common size of its [[bases|QTSQR7130G]].\nRank generalizes the [[rank of a matrix|0ZC9YTXZRY]] and the size of a spanning forest of a graph, and its properties, notably submodularity, characterize matroids.\n\n## Explanations\n\n### L1 human\n\nGiven some of the elements of a matroid, ask how many of them you can keep while staying independent.\nThat number is their rank.\nFor a set of vectors it is the dimension of the space they span.\nFor a set of edges of a graph, keep all the vertices but only these edges.\nThe rank is the number of vertices minus the number of connected pieces.\nIn a triangle, the three edges together have rank $3 - 1 = 2$.\n",
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