Ellipsoids (3): 3D examples, degenerate cases, hyperboloids

Antonio Sala, UPV

Difficulty: ** ,       Relevance: ,      Duration: 08:28

Summary:

This video presents examples of 3D ellipsoids, in order to complete the examples in the videos [ellip1EN] and [ellip2EN].

It also presents degenerate cases when P or Q are not invertible matrices in quadratic forms $x^{T}Px$ or $x^T{Q}^{-1}x$ appearing in ellipsoid expressions. In this case (if the non-zero eigenvalues are positive) cylinders or ellipsoids of lesser dimension are the result.

The last part of the video discusses the case where P has negative eigenvalues, which generate hyperboloids.

*Link to my [whole collection] of videos in English. Link to larger [Colección completa] in Spanish.