I just realized that there is an even more general version of the rules for quadratic forms I posted recently:
$${\rm trace}\left(\ma{A} \cdot \ma{X} \cdot \ma{R} \cdot \ma{X}^{\rm H} \cdot \ma{B}^{\rm H}\right) = {\rm vec}\left(\ma{X}\right)^{\rm H} \cdot \left( \ma{R}^{\rm T} \otimes \ma{B}^{\rm H} \cdot \ma{A} \right) \cdot {\rm vec}\left(\ma{X}\right) $$
Enjoy!
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