Matroid theory

Matroid representation

In the mathematical theory of matroids, a matroid representation is a family of vectors whose linear independence relation is the same as that of a given matroid. Matroid representations are analogous to group representations; both types of representation provide abstract algebraic structures (matroids and groups respectively) with concrete descriptions in terms of linear algebra. A linear matroid is a matroid that has a representation, and an F-linear matroid (for a field F) is a matroid that has a representation using a vector space over F. Matroid representation theory studies the existence of representations and the properties of linear matroids. (Wikipedia).

Matroid representation
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Group representation | Linear span | Matroid rank | Vector space | Finite field | Linear algebra | Finite set | Algebraic matroid | Uniform matroid | Vámos matroid | Reachability | Isomorphism | Binary matroid | Graphic matroid | Algebraic number field | Linear independence | Fano plane | Perles configuration | GF(2) | Rational number | Partition matroid | Matroid | Incidence matrix | Field extension | Dimension (vector space) | Characteristic (algebra) | Gammoid | Field (mathematics) | Cycle (graph theory) | Real number | Family of sets | Algebraic independence | Bijection | Prime number | General position | Matroid minor | Dual matroid | Rota's conjecture | Regular matroid | Directed graph | Matrix (mathematics) | Rank (linear algebra) | Rigidity matroid