= Physical range of a uniaxial nematic order parameter
{title2=$-\tfrac12\leq Q\leq1$}
For $S=\langle3\mathbf s\mathbf s^{\mathsf T}-I\rangle=Q(3\mathbf n\mathbf n^{\mathsf T}-I)$ and unit molecular orientations $\mathbf s$, contraction with $\mathbf n$ gives $2Q=3\langle(\mathbf s\cdot\mathbf n)^2\rangle-1$. Since the squared projection is between zero and one, the displayed bounds follow. The <eigenvalues> in this normalization are $2Q,-Q,-Q$. A differently normalized <nematic order parameter> has correspondingly rescaled bounds; its numerical coefficients cannot be transferred unchanged.
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