So I think the answer to your question is ‘yes*’. In the sense that the ellipse is a function of the unit ball && the matrix A. In this sense you could say that all ellipsoids are linearly-deformed spheres.
But more probably, you would consider the sphere part to be essentially your basis vectors and not terribly informative. All the information is in the matrix. The only important data is the extent along each axis, not the fact that if you set all extents to 1 it happens to be a unit sphere
But more probably, you would consider the sphere part to be essentially your basis vectors and not terribly informative. All the information is in the matrix. The only important data is the extent along each axis, not the fact that if you set all extents to 1 it happens to be a unit sphere