Abstract: Based the concept of Euclidean norm,for two rotational positions represented by 3×3 matrices R₁ and R₂,it is shown that matrices R₂-R₁ and R₂(R₁)^T lead directly to desirable measures of rotational error.Under particular investigation,it is made clear that the body's rotational error can be computed most efficiently through directly calculating the Euclidean norm of the matrix difference ΔR=R₂-R₁.