Matroid

In combinatorial mathematics, a matroid is a structure that captures the essence of a notion of "independence" (hence independence structure) that generalizes linear independence in vector spaces. There are many equivalent ways to define a matroid (that is one way we know the concept is important!); the most significant include those in terms of independent sets, bases, closed sets (flats), the closure operator, circuits (minimal dependent sets), and the rank function.

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Combinatorial: REDIRECT Combinatorics...

Linear independence: In linear algebra, a family of vectors is linearly independent if none of them can be written as a linear combination of finitely many other vectors in the collection. For instance, in three-dimensional Euclidean space R3, the three vectors (1, 0, 0), (0, 1, 0) and (0, 0, 1) are linearly independent...

Vector space: A vector space (or linear space) is the basic object of study in the branch of mathematics called linear algebra....