This video is a continuation of [ellip1EN]. Here, we insist on the meaning of the
diagonalization of a defined positive matrix, to determine semiaxes and their
directions (recovering the diagonal scalings and rotations that generate
it).
The second part of the video discusses alternative ways of representing ellipsoids: as a
quadratic form , as
, or as the image of the
unit sphere by a matrix
(linear map). It also presents the ellipsoid not centered at the origin.
The video [ellip3EN], a continuation of this one, presents 3D examples and degenerate cases of
non-invertible
or .