# Matroid

## Abstraction of linear independence of vectors / From Wikipedia, the free encyclopedia

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In combinatorics, a branch of mathematics, a **matroid** /ˈmeɪtrɔɪd/ is a structure that abstracts and generalizes the notion of linear independence in vector spaces. There are many equivalent ways to define a matroid 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 sets, 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.^{[1]}^{[2]}