5.1 Ellipsoid Algorithm, Part I

We give a high level description of the Ellipsoid Algorithm, and state the Löwner-John theorem.

[covidiotseverywhere]

I didn't exactly get why convexity is required for the Lowner-John Ellipsoid. Why would the ellipsoid not contains the points in K? Wouldn't a concave set K be a subset of the convex set created by the convex combination of vertices of K? So, the convex set would be larger than the concave one

EDIT: It's resolved