Editing Homogeneous coordinates (section)

==Plücker coordinates==
{{Main|Plücker coordinates}}
Assigning coordinates to lines in projective 3-space is more complicated since it would seem that a total of 8
coordinates, either the coordinates of two points which lie on the line or two planes whose intersection is the line,
are required. A useful method, due to [[Julius Plücker]], creates a set of six coordinates as the determinants
{{nowrap|<math>x_i y_j - x_j y_i (1 \le i <  j \le
    4)</math>}} from the homogeneous coordinates of two points {{nowrap|<math>(x_1, x_2,
    x_3, x_4)</math>}} and {{nowrap|<math>(y_1, y_2, y_3,
    y_4)</math>}} on the line. The [[Plücker embedding]] is the generalization of this to create homogeneous coordinates of elements of any dimension <math>m</math> in a projective space of dimension <math>n</math>.<ref>{{harvnb|Wilczynski|1906|p=50}}</ref><ref>{{harvnb|Bôcher|1907|p= 110}}</ref>