 An SVD of formula_2 gives

where formula_62 and formula_63 are orthogonal formula_1 matrices and formula_65 is a formula_1 diagonal matrix with

The diagonal entries of formula_65 are the singular values of formula_2 which, according to the internal constraints of the essential matrix, must consist of two identical and one zero value.Define

and make the following ansatz

Since formula_65 may not completely fulfill the constraints when dealing with real world data (f.e.camera images), the alternative

may help.