HCR - Definition of 'Elementary Rotation'

Given 2 reference frames we define the elementary rotation of the frame $A$ with respect to frame $B$ as the rotation of only one axis of the frames.

The composition of multiple Elementary Rotation Matrix result in a complete Rotation Matrix. ~Ex.:

~ Example: Rotation along the $x$ axis:

We rotate the frame with an angle of $\theta$ along the $x$ axis, as we can see in the second picture we can rewrite the rotation as:

$$R_{x(\theta )}=\left[\begin{array}{ccc}1& 0& 0\\ 0& \cos (\theta )& -\sin (\theta )\\ 0& -\sin (\theta )& \cos (\theta )\end{array}\right]$$

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• ~Example: Other Elementary Rotations:$\begin{array}{l}{R}_{x(\theta )}=\left[\begin{array}{ccc}1& 0& 0\\ 0& \cos (\theta )& -\sin (\theta )\\ 0& -\sin (\theta )& \cos (\theta )\end{array}\right]\\ R_{y(\theta )}=\left[\begin{array}{ccc}\cos (\theta )& 0& \sin (\theta )\\ 0& 1& 0\\ -\sin (\theta )& 0& \cos (\theta )\end{array}\right]\\ R_{z(\theta )}=\left[\begin{array}{ccc}\cos (\theta )& -\sin (\theta )& 0\\ \sin (\theta )& \cos (\theta )& 0\\ 0& 0& 1\end{array}\right]\end{array}$