# Measuring rotation and translation differences between two matrices

I am developing a docking application in which I want to have for every step the difference between the target transformation matrix and the user's transformation matrix. Now I don't have any problem with the coding part but rather with the linear algebra part.

So let's say T is my target transformation matrix, and U is the user's transformation matrix.

To get the difference between the two matrices I do:

(U^-1) * (T) = Difference


Now my matrices are formed with translation, rotation and scaling. My question would be how I should measure the total translation difference as well as the total rotation difference (not interested in the scaling part).

• You could measure how much the transformation differs from the identity transformation in different ways. The easiest would be just an $L_2$ norm of the difference $|M-I|_2$. – mathreadler Aug 16 '15 at 17:02