= Support function of a centred ellipsoid
{title2=$\max_{x^TSx=C}q^Tx=\sqrt{Cq^TS^{-1}q}$}
Let $S$ be a real symmetric positive definite <matrix>, $C>0$ and $q\ne0$. The <Cauchy-Schwarz inequality> in the $S$-weighted <inner product> gives $q^Tx=(S^{-1}q)^TSx\le\sqrt{q^TS^{-1}q}\sqrt{x^TSx}$. Equality is attained by a positive multiple of $S^{-1}q$. Thus the displayed maximum holds. For a translated <ellipsoid>, add $q^Ta$ for its centre $a$. This computes a coordinate extremum without constructing a rotation matrix.
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