# Matroid

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A Matroid is a matrix that ...

**Context:**- It can be a Binary Matroid.
- It can be a Linearly-Separable Matroid.

**See:**Combinatorics, Linear Independence, Vector Space, Linear Algebra, Graph Theory, Topology, Combinatorial Optimization, Network Theory, Coding Theory, Matroid Rank Function.

## References

### 2015

- (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/matroid Retrieved:2015-1-26.
- In combinatorics, a branch of mathematics, a
**matroid**is a structure that captures and generalizes the notion of linear independence in vector spaces. There are many equivalent ways to define a matroid, the most significant being in terms of independent sets, bases, circuits, closed sets or flats, closure operators, and rank functions.Matroid theory borrows extensively from the terminology of 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.

- In combinatorics, a branch of mathematics, a

### 2010

- (Welsh, 2010) ⇒ Dominic J. Welsh. (2010). “Matroid Theory." Courier Corporation,

### 1965

- (Edmonds, 1965) ⇒ Jack Edmonds. (1965). “Minimum Partition of a Matroid Into Independent Subsets." J. Res . Nat . Bur . Standards Sect. B 69
- QUOTE: … A matroid is a (finite) system of elements and sets of elements which satisfies axioms I and 2. For any independence system, any subsystem consisting of a subset A of the elements and all of the independent sets contained in A is an independence system. ...