|Home||Catalog of Oriented Matroids||Catalog of Point Configurations||Catalog of Hyperplane Arrangements||Glossary|
An oriented matroid can be represented (and defined) in several, equivalent ways. The basic axiom systems include vector (or covector) axioms, circuit (or cocircuit) axioms, and chirotopes.
We define here an oriented matroid using the covector axioms: An oriented matroid is a pair of a finite set and a set of sign vectors (called covectors) on for which the following covector axioms (F0) to (F3) are valid:
|(F1)||If then .||(symmetry)|
where if and
there exists such that and for all .