If we take a 3x3 rotational matrix to describe rotation in 3d space. This matrix can be decomposed to three orthogonal Forward, Right and Up vectors. Now if we know just two of these vectors we can derive the third one easily using the cross product of the first two. So if this is the case, it seems to me that it should be possible to optimise these matrices describing 3d rotation to consist only of 6 values, which would be very desirable for computer programs. Why is this not the case?