sentences:  orthogonal matrices with determinant 1, also known as special orthogonal matrices).In this case, one can write (using the above decomposition formula_17)
  
  where formula_19 is a modified formula_20, with the smallest singular value replaced by formula_21 (+1 or -1), and the other singular values replaced by 1, so that the determinant of R is guaranteed to be positive.For more information, see the Kabsch algorithm.