John ellipsoid

The John ellipsoid is a specific type of ellipsoid that is used in the context of convex analysis and optimization. It is associated with the John’s theorem, which deals with the geometry of convex bodies. More formally, the John ellipsoid of a convex body \( K \) in \( \mathbb{R}^n \) is the unique ellipsoid of maximal volume that can be inscribed in \( K \).