The oriented matroid of a finite configuration of points extracts relative position and orientation information from the configuration. An oriented matroid can be described roughly as a matroid in which every basis is equipped with an orientation (Richter-Gebert and Ziegler 1997, p. 112).
Oriented Matroid
See also
Configuration, MatroidExplore with Wolfram|Alpha
References
Björner, A.; Las Vergnas, M.; Sturmfels, B.; White, N.; and Ziegler, G. Oriented Matroids, 2nd ed. Cambridge, England: Cambridge University Press, 1999.Richter-Gebert, J. and Ziegler, G. M. "Oriented Matroids." Ch. 6 in Handbook of Discrete and Computational Geometry (Ed. J. E. Goodman and J. O'Rourke). Boca Raton, FL: CRC Press, pp. 111-132, 1997.Referenced on Wolfram|Alpha
Oriented MatroidCite this as:
Weisstein, Eric W. "Oriented Matroid." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/OrientedMatroid.html