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In mathematics, the John ellipsoid or Löwner-John ellipsoid E associated to a convex body K in n-dimensional Euclidean space R can refer to the n-dimensional ellipsoid of maximal volume contained within K or the ellipsoid of minimal volume that contains K.
Often, the minimal volume ellipsoid is called as Löwner ellipsoid, and the maximal volume ellipsoid as the John ellipsoid. One also refer to the minimal volume circumscribed ellipsoid as the outer Löwner-John ellipsoid and the maximum volume inscribed ellipsoid as the inner Löwner-John ellipsoid.
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