Rotation Matrices

R_{z}^{2} (θ) = [\begin{matrix} \cos θ & - \sin θ \\ \sin θ & \cos θ \end{matrix}]

R_{z}^{2} (0) = [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}]

R_{z}^{2} (90) = [\begin{matrix} 0 & -1 \\ 1 & 0 \end{matrix}]

R_{z}^{2} (180) = [\begin{matrix} -1 & 0 \\ 0 & -1 \end{matrix}]

$R_{x}^{3} (θ) = [\begin{matrix} 1 & 0 & 0 \\ 0 & \cos θ & - \sin θ \\ 0 & \sin θ & \cos θ \end{matrix}]$	$R_{y}^{3} (θ) = [\begin{matrix} \cos θ & 0 & - \sin θ \\ 0 & 1 & 0 \\ \sin θ & 0 & \cos θ \end{matrix}]$	$R_{z}^{3} (θ) = [\begin{matrix} \cos θ & - \sin θ & 0 \\ \sin θ & \cos θ & 0 \\ 0 & 0 & 1 \end{matrix}]$
$R_{x}^{3} (0) = [\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{matrix}]$	$R_{y}^{3} (0) = [\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{matrix}]$	$R_{z}^{3} (0) = [\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{matrix}]$
$R_{x}^{3} (90) = [\begin{matrix} 1 & 0 & 0 \\ 0 & 0 & -1 \\ 0 & 1 & 0 \end{matrix}]$	$R_{y}^{3} (90) = [\begin{matrix} 0 & 0 & -1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{matrix}]$	$R_{z}^{3} (90) = [\begin{matrix} 0 & -1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \end{matrix}]$
$R_{x}^{3} (180) = [\begin{matrix} 1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1 \end{matrix}]$	$R_{y}^{3} (180) = [\begin{matrix} -1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & -1 \end{matrix}]$	$R_{z}^{3} (180) = [\begin{matrix} -1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & 1 \end{matrix}]$
$R_{x}^{3} (270) = [\begin{matrix} 1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & -1 & 0 \end{matrix}]$	$R_{y}^{3} (270) = [\begin{matrix} 0 & 0 & 1 \\ 0 & 1 & 0 \\ -1 & 0 & 0 \end{matrix}]$	$R_{z}^{3} (270) = [\begin{matrix} 0 & 1 & 0 \\ -1 & 0 & 0 \\ 0 & 0 & 1 \end{matrix}]$

$R_{zw}^{4} (θ) = [\begin{matrix} \cos θ & - \sin θ & 0 & 0 \\ \sin θ & \cos θ & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{matrix}]$	$R_{yw}^{4} (θ) = [\begin{matrix} \cos θ & 0 & - \sin θ & 0 \\ 0 & 1 & 0 & 0 \\ \sin θ & 0 & \cos θ & 0 \\ 0 & 0 & 0 & 1 \end{matrix}]$	$R_{xw}^{4} (θ) = [\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & \cos θ & - \sin θ & 0 \\ 0 & \sin θ & \cos θ & 0 \\ 0 & 0 & 0 & 1 \end{matrix}]$
$R_{xy}^{4} (θ) = [\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & \cos θ & - \sin θ \\ 0 & 0 & \sin θ & \cos θ \end{matrix}]$	$R_{xz}^{4} (θ) = [\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & \cos θ & 0 & - \sin θ \\ 0 & 0 & 1 & 0 \\ 0 & \sin θ & 0 & \cos θ \end{matrix}]$	$R_{yz}^{4} (θ) = [\begin{matrix} \cos θ & 0 & 0 & - \sin θ \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ \sin θ & 0 & 0 & \cos θ \end{matrix}]$

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