I think the the expansion of the Kronecker product is "reversed": the explicit matrix expression you wrote should be C kronecker R rather than R kronecker C.
If we take X as a one-observation-per-role matrix then the covariance (of vec(X)) should be R kronecker C.
I think the the expansion of the Kronecker product is "reversed": the explicit matrix expression you wrote should be C kronecker R rather than R kronecker C.
If we take X as a one-observation-per-role matrix then the covariance (of vec(X)) should be R kronecker C.