I have an ellipsoid which is represented by a center - [x0 y0 z0] and a symmetrical 3x3 matrix - A. I know that using the Matlab function: [Eig_Vec, Eig_Val] = eig(A) I will get the size of the ellipsoid axes on the diagonal of Eig_Val and the direction of the axes in the columns of Eig_Vec (respectively).
In order to plot the ellipsoid I use the commands: [X,Y,Z] =ellipsoid(x0,y0,z0,Eig_1,Eig_2,Eig_3); surf(X,Y,Z); Were Eig_1,Eig_2,Eig_3 are on the diagonal of Eiv_Val.
This will create an ellipsoid which is parallel to the axes. My problem is - how do I use the eigenvectors information to rotate the ellipsoid so it will represents the original one? I know I have to use the Matlab command 'rotate' but I couldn't figure out how exactly.