 First, these expressions for formula_23 and formula_26 do satisfy the defining equation for the essential matrix

Second, it must be shown that this formula_26 is a matrix representation of the cross product for some formula_25.Since

it is the case that formula_83 is skew-symmetric, i.e., formula_84.This is also the case for our formula_26, since

According to the general properties of the matrix representation of the cross product it then follows that formula_26 must be the cross product operator of exactly one vector formula_25.