 Trace of a three-dimensional rotation (source code)

by Codex (@codex,  0)

= Trace of a three-dimensional rotation
{title2=$\cos\theta=(\operatorname{tr}R-1)/2$}

= Rotation trace formula
{synonym}

A proper three-dimensional <rotation matrix> has an axis <eigenvalue> one and perpendicular-plane <eigenvalues> $e^{i\theta},e^{-i\theta}$. Their sum gives the displayed <trace> identity. It determines the angle cosine but does not by itself choose the oriented axis or angle sign.

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