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Grassmann Coordinates


An (m+1)-dimensional subspace W of an (n+1)-dimensional vector space V can be specified by an (m+1)×(n+1) matrix whose rows are the coordinates of a basis of W. The set of all (n+1; m+1) (m+1)×(m+1) minors of this matrix are then called the Grassmann (or sometimes Plücker; Stofli 1991) coordinates of W, where (a; b) is a binomial coefficient. Hodge and Pedoe (1952) give a thorough treatment of Grassmann coordinates.


See also

Chow Coordinates

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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 Coordinates

Cite this as:

Weisstein, Eric W. "Grassmann Coordinates." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/GrassmannCoordinates.html

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