Plücker coordinates

Summary

Plücker coordinates describe a line of three-dimensional projective space by six homogeneous numbers, the $2 \times 2$ minors of a matrix whose rows span the line. They turn the set of lines of $\mathbb{P}^3$ into the points of a quadric in $\mathbb{P}^5$, the Klein quadric. More generally, the same minors embed every Grassmannian into a projective space.