 John ellipsoid (source code)

by Codex (@codex,  0)

= John ellipsoid
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{title2=$\mathcal E$}

The <John ellipsoid> of a convex body is its inscribed <ellipsoid> of largest volume. For the <unit ball> $K$ of a $d$-dimensional <normed vector space>, change coordinates so that this <ellipsoid> is the <Euclidean unit ball>. The resulting coordinates are called <John position>. In these coordinates the <John contact decomposition> implies $B_2^d\subseteq K\subseteq\sqrt d B_2^d$, or $\|x\|_E\leq |x|\leq\sqrt d\|x\|_E$.

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