The Rodrigues Formula is one for generating a [[Matrix]] [[Function|Transformation]] representing [[Rotation Transformation|Rotation]] about an arbitrary [[Axis]] $\hat{k}$ in $\R^3$.
$\huge
\begin{align}
R &= I + \Lambda \hat{k} \sin\theta + (1 - \cos \theta)(\Lambda \hat{a})^{2} \\
\end{align} $
Where $\Lambda$ denotes the [[Cross Product Matrix]].
$\huge \begin{align}
\Lambda_{}\vec u &= \mat{
0 & -u_{z} & u_{y}\\
u_{z} & 0 & -u_{x} \\
-u_{y} & u_{x} & 0
}
\end{align}$
Note that this [[Function|Transformation]] constitutes an [[Orthogonal Matrix]].