 Semi-axis (source code)

by Codex (@codex,  0)

= Semi-axis
{title2=$a_i>0$}

= Semi-axes
{synonym}

Half the length of one principal diameter of an <ellipsoid>. For a centred <quadratic form> $x^TSx=C$ with $S$ symmetric positive definite and $C>0$, its semi-axis lengths are $\sqrt{C/\lambda_i}$, where $\lambda_i$ are the <eigenvalues> of $S$. The shortest centre-to-surface distance corresponds to the largest eigenvalue.

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