 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.

 Back to article page