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We can see that in order to minimize J, we need to maximize g(R). This problem can be written in a better and more elegant way by representing rotation matrix R in terms of the quaternion
[[File:Equation29.png|frame|center]]
R can be written in terms of q as<math>R = (q_4^2-q^Tq)I+2qq^T-2q_4[[File:Equation30.png|frame|center]q \times]</math><br \>
Where [q x] is the cross product matrix associated with q
[[File:Equation31.png|frame|center]]