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where a is the vector along axis of rotation. The initial matrix equation now turns out as follows
[[File:Equation48.png|frame|center]]
'''p ''' is being operated on by an invertible matrix. And Gauss elimination could be employed to find its inverse and hence solve for '''p'''. <br \>
Finally, the quaternion is normalised to get an unit quaternion.
[[File:Equation49.png|frame|center]]