Regular matroid

In mathematics, a regular matroid is a matroid that can be represented over all fields.

A matroid is defined to be a family of subsets of a finite set, satisfying certain axioms. The sets in the family are called "independent sets". One of the ways of constructing a matroid is to select a finite set of vectors in a vector space, and to define a subset of the vectors to be independent in the matroid when it is linearly independent in the vector space. Every family of sets constructed in this way is a matroid, but not every matroid can be constructed in this way, and the vector spaces over different fields lead to different sets of matroids that can be constructed from them.

A matroid ${\displaystyle M}$ is regular when, for every field ${\displaystyle F}$, ${\displaystyle M}$ can be represented by a system of vectors over ${\displaystyle F}$.

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