[dellamonica]

Every ellipse can be encoded by the matrix A (and the geometric concept is generalized to arbitrary dimensions).

Not sure I follow the physics analogy though. A unit ball is a specific case of an ellipse where A is the identity matrix. Perhaps the entries of A would be the atoms in this case as they uniquely shape it?

[makerdiety]

How about a software development analogy then?:

A unit ball along with the possibility of doing linear transformations on the unit ball are dependencies for constructing an ellipse.

:)

The physics metaphor is meant to communicate that you can have different materials (like aluminum or air), depending on the combinations or parameters used for a particular ellipsis case. And the physics or dynamics of ellipses would be the study of how the combinations on the dependencies (that is, the atomic elements) create different ellipsis shapes and properties.

[nighthawk454]

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