Plücker Plane Coordinates
Encode a plane with six minors and test whether a perturbed bivector still represents a plane.
Free theory articleEncode a plane with six minors and test whether a perturbed bivector still represents a plane.
Concept & interpretation
Plücker coordinates encode a subspace of a vector space using alternating forms. Specifically, for a 2-dimensional plane in a 4-dimensional space, we can represent the plane using six minors.
Experiment
You can test the Plücker relation and bivector norms using the interactive tool at https://riano.app/module/plucker-plane-coordinates.
- Set the Rows control to
Genericand Row scale to1. Observe that the Plücker relation is 0, and the status is Decomposable. - Change Minor perturbation to
1. This modifies p34, breaking the relation. The status becomes Nondecomposable, meaning the new six values no longer represent a simple 2-plane. - Change Rows to
Dependent. Observe that the relation is 0, but the norm is also 0, yielding aZero bivectorstatus.