= Root hyperplane
{title2=$\ker\alpha=\alpha^\perp$}
The hyperplane perpendicular to a <root of a root system> is its root hyperplane, interpreted as the kernel of the associated linear functional on the Cartan space. The corresponding <reflection> is $s_\alpha(v)=v-2\langle v,\alpha\rangle\alpha/\langle\alpha,\alpha\rangle$. For the <B2 root system>, the four distinct hyperplanes are the two coordinate axes and the two diagonals; their reflections generate the signed-permutation <Weyl group> of order eight.
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