An interpretation of this would be:
Pick your rotation around ONE axis

You will affect two of the three axes

Rotation about a 2D space, keep other one constant

In short, you are working to rotate utilizing two axes at a time (mini-proof is notice the columns with the 1s and the 2D rotation like elements in the matrix)

yirenng

@ochan1 -- thank you!

yirenng

For $\mathbf{R}_y(\alpha)$, where would the red arrow go? And how about for $\mathbf{R}_z(\alpha)$. Why does the top-right $\sin(\alpha)$ in the second matrix lack a negative sign?

An interpretation of this would be: Pick your rotation around ONE axis

You will affect two of the three axes

Rotation about a 2D space, keep other one constant

In short, you are working to rotate utilizing two axes at a time (mini-proof is notice the columns with the 1s and the 2D rotation like elements in the matrix)

@ochan1 -- thank you!

For $\mathbf{R}_y(\alpha)$, where would the red arrow go? And how about for $\mathbf{R}_z(\alpha)$. Why does the top-right $\sin(\alpha)$ in the second matrix lack a negative sign?