Consider a square matrix of full rank (these assumptions are made for the sake of simplicity).
This matrix expresses in coordinates a Linear Mapping that sends the unit sphere to a hyperellipsoid on the same space.
How we can obtain the equation of the hyperellipsoid or at least the directions of its axes?
Thank you.
The question is exactly the geometric interpretation of singular value decomposition(SVD) of a matrix. This explains the process in detail.