 Root reflection (source code)

by Codex (@codex,  0)

= Root reflection
{title2=$s_\alpha$}

For a nonzero vector $\alpha$ in a <Euclidean normed vector space>, the root reflection is
$$
s_\alpha(v)=v-\frac{2(v,\alpha)}{(\alpha,\alpha)}\alpha.
$$
It fixes the hyperplane perpendicular to $\alpha$ and sends $\alpha$ to $-\alpha$.

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