An 
-dimensional
subspace 
of an 
-dimensional vector space 
can be specified by an 
matrix whose rows
are the coordinates of a basis of 
. The set of all 
minors of this matrix are then called the Grassmann (or sometimes Plücker;
Stofli 1991) coordinates of 
, where 
is a binomial coefficient.
Hodge and Pedoe (1952) give a thorough treatment of Grassmann coordinates.
Grassmann Coordinates
See also
Chow CoordinatesExplore with Wolfram|Alpha
References
Hodge, W. V. D. and Pedoe, D. Methods of Algebraic Geometry. Cambridge, England: Cambridge University Press, 1952.Stofli, J. Oriented Projective Geometry. New York: Academic Press, 1991.Wilson, W. S.; Chern, S. S.; Abhyankar, S. S.; Lang, S.; and Igusa, J.-I. "Wei-Liang Chow." Not. Amer. Math. Soc. 43, 1117-1124, 1996.Referenced on Wolfram|Alpha
Grassmann CoordinatesCite this as:
Weisstein, Eric W. "Grassmann Coordinates." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/GrassmannCoordinates.html