Hello Fabian,
You need to find the rotation matrix (in your case Q) from equation
Q*A*Q^T = B
After a little bit of algebra, I was able to find the following way to find rotation matrix:
[Da, eigA] = eig(A); % Find eigenvectors and eigenvalues of A
[Db, eigB] = eig(B); % Find eigenvectors and eigenvalues of B
Q = Db'*Da; % This relation can be derived if we substitute B = Db^T*eigB*Db and A = Da^T*eigA*Da in above equation and noting that eigA and eigB are same because it is a similarity transform
disp('QAQ^T'), disp(Q*A*Q'); % Check if Q*A*Q^T gives B
disp('B'), disp(B)
Now you can find out the angle of rotation and axis of rotation from the rotation matrix itself (i.e. in your case only "Q" matrix is enough).
The rotation angle is given by following formula:
rotation_angle = acos(0.5*trace(Q));
I carried out above steps on the example provided by you and got the correct result. I am attaching the script for reference. Note that for 3-D case, you need to use the following formula:
rotation_angle = acos(0.5*(trace(Q)-1));
I hope this helps and answers your question.
Regards,
Vaibhav
