Reverse Rotation Matrices

These matrices rotate a set of crystal field parameters (or Stevens operators) by $\Theta_1$=90$^o$ and $\Phi_1$=90$^o$ and again by $\Theta_2$=90$^o$ and $\Phi_2$=90$^o$.

$$\stackrel{=}{\mathbf S^{-1}}_2(\pi/2,\pi/2) = \left( \begin... ...0 & 0 & 0 \\ 0 & 0 & -3/2 & 0 & -1/2 \\ \end{array} \right)$$ (181)

$$\stackrel{=}{\mathbf S^{-1}}_4(\pi/2,\pi/2) = \left( \begin... ...& 0 & 0 & 0 & 35/8 & 0 & 7/8 & 0 & 1/8 \\ \end{array} \right)$$ (182)

$$\stackrel{=}{\mathbf S^{-1}}_6(\pi/2,\pi/2) = \left( \begin... ... 0 & -33/32 & 0 & % -11/32 & 0 & -1/32 \\ \end{array} \right)$$ (183)