What does a transformation between ellipsoids mean to you? Why do you need some special function anyway?
An ellipsoid is defined in any number of dimensions by a simple quadratic form, thus essentially:
(X-X0)' * H * (X-X0) == 1
where H is an nxn non-negative definite matrix. (If H is singular, then the ellipsoid has zero volume, and it lies contained in some lower dimensional planar subspace. But it is still technically an ellipsoid.) X0 is a vector that defines the center of the ellipsoid, and X is an nx1 vector. That completely defines the surface of the ellipsoid. If you want to include the points contained inside the ellipsoid, then the equality becomes an inequality.
If you have multiple ellipsoids, then you just have different center points and different matrices H. You know everything about an ellipsoid that you need to know, if you know the matrix H and the vector X0. At least, you can compute anything from those two variables.
So in that context, what do you want to know about a "transformation" between ellipsoids? What might you hope some function would do for you in that context?
