Theorem: Gr(2,4) Plücker identity p_12*p_34 - p_13*p_24 + p_14*p_23 = 0 (algebraic identity in 2x4 matrix)

Theorem (Gr(2,4) Plücker algebraic-identity canonical): for any 2x4 matrix with rows a = (a_1, a_2, a_3, a_4), b = (b_1, b_2, b_3, b_4), the 2x2 minors p_{ij} = a_i b_j - a_j b_i satisfy the Plücker relation p_{12} p_{34} - p_{13} p_{24} +…